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Find the area of the composite figure

Find the area of the composite figure-example-1
User Sevenflow
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2 Answers

7 votes
Greetings and Happy Holidays!

Let Statements:

Let l represent the length of square
Let w represent the width of a square
Let b represent the base of a triangle
Let h represent the height of a triangle
Let r represent the radius of a semi-circle

Formula for the area of a square:
A=lw

Input the values of the variables:

A=(18)(8)

The Area of the Square is:

\boxed {A=144}

Formula for the area of the Triangle(s):
A=(bh)/(2)

Input the values of the variables:

A=2(((5)(8))/(2))

Solve using the order of operations.

A=2((40)/(2))


A=2(20)

The Area of the Triangle is:

\boxed {A=40}

Formula for the area of a semi-circle:
A=(\pi r^(2))/(2)

Input
the values of the variables:

A=(\pi (9)^(2))/(2)

Solve using the order of operations.

A=((81)\pi)/(2)


A=(254.469)/(2)

The Area of the Semi-Circle is:

\boxed {A=127.235}

Now, to find the total area of the composite shape, we must add up all the values:

A=A_(square)+A_(triangles)+A_(semi-circle)

Input the values of the variables:

A=(144)+(40)+(127.235)

Solve using the order of operations.

A=(184)+(127.235)

The Answer Is:

\boxed {A=311.235}

The total area of the composite shape is 311.235 ft²

I hope this helped!
-Benjamin

User Kimmi
by
8.4k points
3 votes
Area of the two triangles = 5*8 = 40 ft^2
Area of rectangle = 18*8 = 144 ft^2
Area of semicircle = 0.5*π*9^2 = 40.5π ft^2

Total area = 40 + 144 + 40.5π = 311 ft^2 (3 s.f.)
User Kshitij Godara
by
8.1k points

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