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): $A=\frac{bh}{2}$

Input the values of the variables:
$A=2(\frac{(5)(8)}{2})$

Solve using the order of operations.
$A=2(\frac{40}{2})$

$A=2(20)$

The Area of the Triangle is:
$\boxed {A=40}$

Formula for the area of a semi-circle: $A=\frac{\pi r^{2}}{2}$

Input the values of the variables:
$A=\frac{\pi (9)^{2}}{2}$

Solve using the order of operations.
$A=\frac{(81)\pi}{2}$

$A=\frac{254.469}{2}$

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.)