Question

Find the area of the composite figure

Answer 1

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

Answer 2

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.)