solving right triangle find the missing side. round to the nearest tenth number 15
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To solve the triangle we are going to first find the measures of all the angles:
[tex]\begin{gathered} A=47\text{\degree} \\ B=90\text{\degree}\Rightarrow\text{ Because is a right triangle} \\ A+B+C=180\text{\degree} \\ \text{Because the sum of the internal angles of a triangle is 180 degrees} \\ 47\text{\degree}+90\text{\degree}+C=180\text{\degree} \\ 137\text{\degree}+C=180\text{\degree} \\ \text{ Subtract 137\degree from both sides of the equation} \\ 137\text{\degree}+C-137\text{\degree}=180\text{\degree}-137\text{\degree} \\ C=43\text{\degree} \end{gathered}[/tex]Now to find the measures of the sides you can use trigonometric ratios because it is a right triangle:
Side a: you can use the trigonometric ratio tan(θ)
[tex]\tan (\theta)=\frac{\text{ opposite side}}{\text{adjacent side}}[/tex][tex]\begin{gathered} \tan (47\text{\degree})=\frac{a}{28} \\ \text{ Multiply by 28 from both sides of the equation} \\ \tan (47\text{\degree})\cdot28=\frac{a}{28}\cdot28 \\ 30=a \end{gathered}[/tex]Side b or side x: you can use the trigonometric ratio cos(θ)
[tex]\cos (\theta)=\frac{\text{adjacent side}}{\text{hypotenuse}}[/tex][tex]\begin{gathered} \cos (47\text{\degree})=\frac{28}{b} \\ \text{ Multiply by b from both sides of the equation} \\ \cos (47\text{\degree})\cdot b=\frac{28}{b}\cdot b \\ \cos (47\text{\degree})\cdot b=28 \\ \text{ Divide by cos(47\degree) from both sides of the equation} \\ \frac{\cos (47\text{\degree})\cdot b}{\cos (47\text{\degree})}=\frac{28}{\cos (47\text{\degree})} \\ b=\frac{28}{\cos(47\text{\degree})} \\ b=41.1 \end{gathered}[/tex]Therefore, when solving the triangle you have
[tex]\begin{gathered} A=47\text{\degree} \\ B=90\text{\degree} \\ C=43\text{\degree} \\ a=30 \\ b=41.1 \\ c=28 \end{gathered}[/tex]and the missing side is
[tex]\begin{gathered} b=x \\ x=41.1 \end{gathered}[/tex]
Related Questions
A rectangular prism has volume 10,878 cubic feet, length 7 feet, and height 42 feet. Find its width, in feet.
Answers
Answer: The width is 37 feet
Given data
Volume = 10, 878 cubic feet
Length = 7 feet
Height = 42 feet
width = ?
Let width = w
Volume of the rectangular prism = l x w x h
10, 878 = 7 x 42 x w
10, 878 = 294 x w
10, 878 = 294w
Divide both sides by 294
10, 878 /294 = 294w/294
w = 10, 878 / 294
w = 37 feet
Therefore, the width is 37 feet
Click an item in the list or group of pictures at the bottom of the problem and, holding the button down, drag it into thecorrect position in the answer box. Release your mouse button when the item is place. If you change your mind, dragthe item to the trashcan. Click the trashcan to clear all your answers.Indicate in standard form the equation of the line through the given points.K(6,4), L(-6,4)
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The equation between two points is given as:
[tex]y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)[/tex]Plugging the values of the points given we have:
[tex]\begin{gathered} y-4=\frac{4-4}{-6-6}(x-6) \\ y-4=\frac{0}{-12}(x-6) \\ y-4=0(x-6) \\ y-4=0 \\ y=4 \end{gathered}[/tex]Therefore the equation in standar form is:
[tex]y=4[/tex]Caleb's recipe calls for 4.4 cups of an ingredient. His measuring bowl only has measurements marked in liters. Caleb knows that one cup is approximately 240 milliliters. Determine the number of liters of that ingredient that Caleb needs for his recipe.
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For points K (-6,6) and P (-3,-2), find the following:m:| m:I m:Distance:Equation of a line 1:
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From the question
We are given the points
[tex]K(-6,6),P(-3,-2)[/tex]Finding the slopre, m
Slope is calculated using
[tex]m=\frac{y_{2_{}}-y_1}{x_2-x_1}[/tex]From the given points
[tex]\begin{gathered} x_1=-6,y_1=6 \\ x_2=-3,y_2=-2 \end{gathered}[/tex]Therefore,
[tex]\begin{gathered} m=\frac{-2-6}{-3-(-6)} \\ m=\frac{-8}{-3+6} \\ m=\frac{-8}{3} \end{gathered}[/tex]Therefore, m = -8/3
The next thing is to find
[tex]\mleft\Vert m\mright?[/tex]A slope parallel to m
For parallel lines, slopes are equal
Therefore,
[tex]\mleft\Vert m=-\frac{8}{3}\mright?[/tex]Next, we are to find
[tex]\perp m[/tex]A slope perpendicular to m
For perpendicular lines, the product of the slopes = -1
Therefore
[tex]\perp m=-\frac{1}{m}[/tex]Hence,
[tex]\begin{gathered} \perp m=-\frac{1}{-\frac{8}{3}} \\ \perp m=\frac{3}{8} \end{gathered}[/tex]Therefore,
[tex]\perp m=\frac{3}{8}[/tex]Next, we are to find the distance KP
Using the formula
[tex]KP=\sqrt[]{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]This gives
[tex]\begin{gathered} KP=\sqrt[]{(-3-(-6))^2+(-2-6)^2} \\ KP=\sqrt[]{3^2+(-8)^2} \\ KP=\sqrt[]{9+64} \\ KP=\sqrt[]{73} \end{gathered}[/tex]Therefore,
[tex]\text{Distance }=\sqrt[]{73}[/tex]Next, equation of the line
The equation can be calculated using
[tex]\frac{y-y_1}{x-x_1}=m[/tex]By inserting values we have
[tex]\begin{gathered} \frac{y-6}{x-(-6)}=-\frac{8}{3} \\ \frac{y-6}{x+6}=-\frac{8}{3} \\ y-6=\frac{-8}{3}(x+6) \\ y-6=-\frac{8}{3}x-6(\frac{8}{3}) \\ y-6=-\frac{8}{3}x-16 \\ y=-\frac{8}{3}x-16+6 \\ y=-\frac{8}{3}x-10 \end{gathered}[/tex]Therefore the equation is
[tex]y=-\frac{8}{3}x-10[/tex]For the function h(x) defined below . Find the function f(x) and g(x)
Answers
ANSWER:
1st option.
[tex]f\left(x\right)=x^3\text{ and }g\left(x\right)=\frac{x+2}{x}[/tex]STEP-BY-STEP EXPLANATION:
We have the following composite function obtained from two functions:
[tex]h(x)=\:\left(f\circ g\right)\left(x\right)=\left(\frac{x+2}{x}\right)^3[/tex]We can determine the functions as follows:
[tex]\begin{gathered} \left(f\circ g\right)\left(x\right)=f\left(g\left(x\right)\right) \\ \\ f\left(g\left(x\right)\right)=\left(\frac{x+2}{x}\right)^3 \\ \\ g(x)=\frac{x+2}{x},\text{ therefore} \\ \\ f(x)=x^3 \end{gathered}[/tex]Therefore, the correct answer is the 1st option.
In ΔIJK, k = 53 cm, j = 66 cm and ∠J=64°. Find all possible values of ∠K, to the nearest 10th of a degree.
Answers
The value of ∠K is 46.2° as the definition of angle is "An angle is created by joining two line segments at one point, or we can say that an angle is the combination of two line segments at a common endpoint".
What is angle?An angle is created by joining two line segments at one point, or we can say that an angle is the combination of two line segments at a common endpoint. When two straight lines or rays intersect at a single endpoint, an angle is created. The vertex of an angle is the location where two points come together. The Latin word "angulus," which means "corner," is where the word "angle" originates. Based on measurement, there are different kinds of angles in geometry. The names of fundamental angles include acute, obtuse, right, straight, reflex, and full rotation. A geometrical shape called an angle is created by joining two rays at their termini. In most cases, an angle is expressed in degrees.
Here,
Side i = 68.91521 cm
Side j = 66 cm
Side k = 53 cm
Angle ∠I = 69.8°
Angle ∠J = 64°
Angle ∠K = 46.2°
∠K= sin⁻¹(k·sin(J)/j)
=sin⁻¹(53.(sin 64°)/66)
=46.2°
Since the definition of an angle is "An angle is created by joining two line segments at one point, or we can say that an angle is the combination of two line segments at a common endpoint," the value of ∠K is 46.2°.
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please help with this question
Answers
if each u it cube has edge's of length 1/2 foot, what is the volume of the blue-outlined prism
we have that
the volume of each cube is equal to
V=(1/2)^3
V=1/8 ft3
the rectangular prism volume is equal to
calculate the volume by the numbers of cube
so
V=(5)(2)(2)=20 cubes
Multiply by the volume of each cube
20*(1/8)=2.5 ft3
the volume of the rectangular prism is 2.5 ft3
which of the following is most likely to represent a fixed rate, secured debit?A- Student loanB- Credit CardC- Loan from a friend D- dealer-finaced auto loan
Answers
D because financing has a fixed rate
a friend's loan has no rate
the credit card varies the rate while you are using it
The student loan has no financing
Type the correct answer in the box. Use numerals instead of words.The expression x^2 - 12x + 36 factors to (x - )^2
Answers
Explanation: Here we have a factorization problem and the way we solve it depends on the complexity and degree of the equation. We can see our equation is a simple quadratic function so we will use a simple method to solve it.
Step 1: Let's take a look at the illustration bellow
Step 2: As we can see above, we just need to find a way to represent the second term as a sum and the last term as multiplication using the same numbers.
Result: Once we found that this number is -6 so we can represent our factor as
[tex](x-6)^2[/tex]And that is our final answer.
A boy at an amusement park has 65 ride tickets. Each ride on the roller coaster costs 7 tickets. After riding the roller coaster as many times as he can, how many tickets will the boy have left?
Answers
ANSWER
[tex]32\text{ tickets}[/tex]EXPLANATION
The group consists of 4 friends and each friend has 12 tickets.
Each friend uses 4 tickets to ride the roller coaster.
To find the number of tickets each friend has after the ride, subtract the number of tickets used for the ride from the number of tickets each friend had initially.
That is:
[tex]\begin{gathered} \Rightarrow12-4 \\ 8 \end{gathered}[/tex]Now, to find the number of tickets the group has, multiply the number of friends in the group by the number of tickets left:
[tex]\begin{gathered} 4\cdot8 \\ 32\text{ tickets} \end{gathered}[/tex]*DUE TODAY* ANSWER ASAP Olivia has read 40 pages of a 70 page book, 60 pages of an 85 page book and 43 of a 65 page book. What is the percentage of pages Olivia has not read? PLEASE GIVE ME A STEP BY STEP EXPLANATION PLEASE!
Answers
STEP2: turn all of the fractions you have just made into percentages ( divide the numerator by the denominator then, times by 100)
STEP 3: add all of the percentages up and put the sum of them all over 300 ( e.g each percentage added up / 300 )
STEP 4: turn that fraction you just made back into a percentage then that should be your answer!!!
If you need any more help just ask me!
The length of an arc of a circle is 5/3 pi feet. Find the measure of the angle that subtends (forms)the arc if the diameter is 18 feet.
Answers
EXPLANATION
We are given the following parameters:
Length of arc= 5/3pi
Diameter = 18 feet
Therefore, radius =18/2 = 9 feets
The formula for the length of the arc is given below.
[tex]\text{length of arc =}\frac{\theta}{360}\times2\pi r^{}[/tex]We will substitute the given parameters into the formula above to get the measure of the angle.
[tex]\begin{gathered} \frac{5}{3}\pi=\frac{\theta}{360}2\pi\times9^{} \\ \frac{5}{3}\pi=\frac{18\theta}{360}\pi \\ crossmultiply\text{ } \\ 3\times18\theta\pi=360\times5\pi \\ 54\theta\pi=1800\pi \\ \text{Divide both sides by 54}\pi \\ \theta=\frac{1800\pi}{54\pi} \\ \theta=33.3^0 \end{gathered}[/tex]Therefore, the measure of the angle is
[tex]\theta=33.3^0[/tex]Z + 24 = -33one step equation
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We solve as follows:
[tex]z=-57[/tex]We operate like terms after substracting 24 from each side of the function.
Use the circle graph below to answer each question. 1. What percent of the Milton's budget is for rent? 2. What percent of the Milton's budget is for clothes? 3. If the Milton's have a $2,000 budget, how much of that budget will go in savings? 4. If the Milton's have a $2,000 budget, how much of that budget will go towards food? 5. If the Milton's have a $2,000 budget, how much of that budget will go towards misc items?
Answers
We are given the Pie chart of Milton's family budget with the following detail:
Food = 33%
Rent = 25%
Savings = 6%
Clothes = 15%
Misc = 21%
1. The percentage of the budget allocated to rent is 25%
2. The percentage of the budget allocated to clothes is 15%
3.
If the budget is $2,000, the amount allocated to Savings is:
[tex]\begin{gathered} Savings=6\text{\%}\times\text{\$}2,000 \\ Savings=\frac{6}{100}\times2,000 \\ Savings=\text{ \$}120 \end{gathered}[/tex]4.
If the budget is $2,000, the amount allocated to food is:
[tex]\begin{gathered} Food=33\text{\%}\times\text{\$}2,000 \\ Food=\frac{33}{100}\times2,000 \\ Food=\text{\$}660 \end{gathered}[/tex]5.
If the budget is $2,000, the amount allocated to Misc is:
[tex]\begin{gathered} Misc=21\text{\%}\times\text{\$}2,000 \\ Misc=\frac{21}{100}\times2,000 \\ Misc=\text{\$}420 \end{gathered}[/tex]18 18 After bisecting the original angle, there are two angles that each measure 18°. Which statement is true? A) The original angle of 2° was bisected into two congruent angles. B) The original angle of 9° was bisected into two congruent angles. Eliminate The original angle of 36° was bisected into two congruent angles. D) The original angle of 72° was bisected into two congruent angles.
Answers
After bisecting the original angle, there are two angles that each measure 18°. Which statement is true? A) The original angle of 2° was bisected into two congruent angles. B) The original angle of 9° was bisected into two congruent angles. Eliminate The original angle of 36° was bisected into two congruent angles. D) The original angle of 72° was bisected into two congruent angles.
we know that
when bisecting an angle, the angle is divided into two equal parts
so
The original measure of the angle is
18(2)=36 degrees
therefore
The statement that is true is
The original angle of 36° was bisected into two congruent anglesy=2/3 × + 4. use this equation to find y for the following values of x. x=0
Answers
a) for x = 0
y = (2/3) x 0 + 4
y = 0 + 4
y = 4
b) x = 3
y = (2/3) x 3 + 4
y = 6/3 + 4
y = 2 + 4
y = 6
c) x = 9
y = (2/3) x 9 + 4
y = 18/3 + 4
y = 6 + 4
y = 10
d) x = -9
y = (2/3) x (-9) + 4
y = -18/3 + 4
y = - 6 + 4
y = -2
e) x = 10
y = (2/3) x 10 + 4
y = 20/3 + 4
y = 32/3
f) x = 1/2
[tex]\begin{gathered} y\text{ = }\frac{2}{3}\text{ x }\frac{1}{2}\text{ + 4} \\ y\text{ = }\frac{1}{3}\text{ + 4} \\ y\text{ = }\frac{1\text{ + 12}}{3} \\ y\text{ = }\frac{13}{3} \end{gathered}[/tex]Find the equation of the line that contains the points (2,4) and (8,9). Write the equation in the form y=mx+b and identify m and b.m=b=
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Find the equation of the line that contains the points (2,4) and (8,9). Write the equation in the form y=mx+b and identify m and b.
step 1
Find the slope
m=(9-4)/(8-2)
m=5/6step 2
Find the equation in slope-intercept form
y=mx+b
we have
m=5/6
point (2,4)
substitute and solve for b
4=(5/6)(2)+b
4=(5/3)+b
b=4-5/3
b=7/3therefore
y=(5/6)x+7/3the dot is on the secomd line if you cant see it
Answers
The fraction of the hour joey used for practicing the piano can be gotten from the gaps in the number line.
Since there are 3 equal gaps in the number line , this denotes the fraction of the hour that each gap would represent is
[tex]\frac{1}{3}[/tex]This implies that the first point is = 0
This implies that the second point is = 1/3
This implies that the third point is = 2/3
This implies that the fourth point is = 1
In conclusion, the answer is B for the second point.
A patient takes three 25 mg capsules a day. How many milligrams is he taking daily?
Answers
Given:
A patient takes three 25 mg capsules a day.
[tex]3\times25\text{ mg=75mg}[/tex]Answer: A patient is taking 75 mg capsules every day.
A pound of pistachios cost 6.60. and you buy 2.75 pounds
Answers
By performing some simple mathematical operations, we know that the total cost of 2.75 pounds of pistachios is $18.15.
What are mathematical operations?An operation is a function in mathematics that transforms zero or more input values into a clearly defined output value. The operation's arity is determined by the number of operands. The rules that specify the order in which we should solve an expression involving many operations are known as the order of operations. PEMDAS stands for Parentheses, Exponents, Multiplication, Division, Addition Subtraction (from left to right).
So, the total cost will be:
1 pound of pistachios costs $6.60.We purchased 2.75 pounds.Then, the total cost will be:
6.60 × 2.75$18.15
Therefore, by performing some simple mathematical operations, we know that the total cost of 2.75 pounds of pistachios is $18.15.
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Correct question:
A pound of pistachios costs $6.60. and you buy 2.75 pounds. What is the total cost?
A regular polygon with 9 sides (a nonagon) has a perimeter of 72 inches. What is the area of this polygon? Provide mathematical evidence.
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The perimeter of the regular nonagon is 72 inches, the length of each side can be determined as,
[tex]\begin{gathered} P=9s \\ 72=9s \\ s=8\text{ inches} \end{gathered}[/tex]The diagram can be drawn as,
The value of apopthem a can be determined as, where n is the number of sides,
[tex]\begin{gathered} a=\frac{s}{2\tan (\frac{180^{\circ}}{n})} \\ =\frac{8}{2\tan20^{\circ}} \\ =10.98\text{ in} \end{gathered}[/tex]The area can be determined as,
[tex]\begin{gathered} A=\frac{P\times a}{2} \\ =\frac{72\text{ inches}\times10.98\text{ inches}}{2} \\ =395.63in^2 \end{gathered}[/tex]Thus, the required area of the polygon is 395.63 square inches.
Which of the following tables corresponds to the equation below?
Answers
Solution:
Given the equation;
[tex]y=\frac{1}{4}(4^x)[/tex]We would create a table of values such that x ranges from 0 to 5;
[tex]\begin{gathered} x=0; \\ \\ y=\frac{1}{4}(4^0)=\frac{1}{4} \\ \\ (0,\frac{1}{4}) \\ \\ x=1; \\ \\ y=\frac{1}{4}(4^1)=1 \\ \\ (1,1) \\ \\ x=2; \\ \\ y=\frac{1}{4}(4^2)=4 \\ \\ (2,4) \end{gathered}[/tex]Then;
[tex]\begin{gathered} x=3; \\ \\ y=\frac{1}{4}(4^3)=16 \\ \\ (3,16) \\ \\ x=4; \\ \\ y=\frac{1}{4}(4^4)=64 \\ \\ (4,64) \\ \\ x=5; \\ \\ y=\frac{1}{4}(4^5)=256 \\ \\ (5,256) \end{gathered}[/tex]Thus, the correct table is;
Answer:
its D
Step-by-step explanation:
3/4 divided by 2/3 using fractions
Answers
To solve this divition we can write it like:
[tex]\frac{\frac{3}{4}}{\frac{2}{3}}[/tex]So now we can multiplicate the numerator of the first fraction with the denominatior of the second fraction, and put the resould in the numerator of the quationt, ans the same operation for the numeratior with the numerator of the secon fraction and the denominator of the first fraction so:
[tex]\frac{3\cdot3}{4\cdot2}=\frac{9}{8}[/tex]-8, {0, -3, 1, -1}, {-1, 1, -2}, {3, -5, 4, -1}, {4, -2, 2}
Answers
Solution
17. -8
18. 0, -3 ,1 , -1
19. -1 ,1 ,-2
20. 3, -5 ,4 ,-1
21. 4, -2. 2
3 view. writing simplity expressions The volume of a cube is calculated by multiplying all three side lengths. If a cube has a side of 16 cm, which expression can be used to calculate the volume? A. 161 B. 167 C. 162 D. 164 에 2y Click to add speaker notes
Answers
If we have a cube with a side length of 16 cm, we can calculate the volume as the length side powered to the 3rd or multiplying the side length 3 times:
[tex]V=l\cdot l\cdot l=l^3=16^3[/tex]Answer: V = 16^3 (Option C).
John flew a kite. He started flying the cat at 2:20 p.m. and ended at 3:14 p.m. How many minutes did John fly a kite?A. 47 minutesB. 50 minutesC. 54 minutesD. 55 minutes
Answers
Given data:
The initial time is t=2:20 pm.
The final timme is t'=3:14 pm.
The time during which kite fly is,
[tex]\begin{gathered} T=3\colon14-2\colon20 \\ =54\text{ min} \end{gathered}[/tex]Thus, option (C) is correct.
given: s is the midpoint of QR , QR , PS and angle RSP and angle QSP are right angles prove PR is congruent to PQ
Answers
∆RSP ≈ ∆QSP through SAS congruency theorem. PR is congruent to PQ.
Given that,
S being the midpoint of QR
SR = QS (∵ midpoint)
PS = PS (common side/reflexive property)
Two right triangles are congruent due to
∵ PS ≅ PS (SAS congruency)
According to the SAS rule, two triangles are said to be congruent if any two sides and any angle contained between the sides of one triangle are equal to the second triangle's two sides and angle between its sides correspond to the first triangle's.
QS ≅ PS
Thus, ∆RSP ≈ ∆QSP through SAS congruency.
While PQ = PR (by CPCT).
Hence, proved.
Therefore, ∆RSP ≈ ∆QSP through SAS congruency theorem. PR is congruent to PQ.
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6y-(2y-5)=29 step by step
Answers
The given expression is
[tex]6y-(2y-5)=29[/tex]First, we use the distributive property to solve the parenthesis, we have to multiply the negative sign with each term inside the parenthesis.
[tex]6y-2y+5=29[/tex]We reduce like terms, 6y and -2y are like terms in this case,
[tex]4y+5=29[/tex]Then, we subtract 5 on each side.
[tex]\begin{gathered} 4y+5-5=29-5 \\ 4y=24 \end{gathered}[/tex]At last, we divide the equation by 4.
[tex]\begin{gathered} \frac{4y}{4}=\frac{24}{4} \\ y=6 \end{gathered}[/tex]Therefore, the solution is 6.How do I go about solving it. What would the answer be?
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The given sum is
[tex]\sum ^9_{k\mathop=4}(5k+3)[/tex]This means we have to replace k = 4, 5, 6, 7, 8, 9, and then we sum
[tex]\begin{gathered} (5\cdot4+3)+(5\cdot5+3)+(5\cdot6+3)+(5\cdot7+3)+(5\cdot8+3)+(5\cdot9+3) \\ 20+3+25+3+30+3+35+3+40+3+45+3=213 \\ \end{gathered}[/tex]Hence, the sum is equal to 213. The right answer is C.ABC and BCD are identical triangles. The overlapping area is 19cm . Find the area ofthe shaded figure.
Answers
The area of the shaded figure is 45 [tex]cm^{2}[/tex]
It is given that ABC and BCD are identical triangles and the overlapping area is 19[tex]cm^{2}[/tex]
Now, to evaluate the area of the shaded figure, we will calculate the area of the two triangles ABC and BCD, then we will subtract the overlapping area from it.
So, by evaluating the figure, it comes out that the length of the triangle is 4 units and 1 unit is 2cm.
So, Height of the triangle = 4 * 2 cm = 8 cm
And the base of the triangle is 3 units, then,
Base of the triangle = 3* 2 cm = 6 cm
The area of the triangle = 1/2 * base* height
Area of triangle ABC = [tex]\frac{1}{2} *8*6 = 24cm^{2}[/tex]
The area of both the triangles = area(ABC) +area(BCD)
Since two the triangles are identical, their areas are also identical,
So, the Area of both the triangles = 2*area(ABC) = 2*24 = 64[tex]cm^{2}[/tex]
Now, The area of the shaded figure = area(ABC) +area(BCD) - overlapping area.
The area of the shaded figure = 64 - 19 = 45 [tex]cm^{2}[/tex]
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