Question

The compound shape below is formed from a semicircle and a rectangle.

Calculate the area of the compound shape.
Give your answer in cm² to 1 d.p.
16 cm
5 cm

Answer 1

`180.5cm^(2)` (Rounded to nearest 1 d.p)

Explanation:

For this question, we can split the compound shape into 2 basic shapes, which is a semicircle and rectangle.

Area of semicircle

Formula =
`(1)/(2) \pi r^(2)`

Area =
`(1)/(2) \pi (8)^(2)` =
`32\pi cm^(2)`

Note: We use 8cm as the formula wants the radius, not the diameter (16cm in this case)

Area of rectangle

Formula = Length x Width

Area = 5 x 16 = 80
`cm^(2)`

Area of compound shape

= Area of semicircle + Area of rectangle

=
`32\pi cm^(2) + 80cm^(2)`

=
`180.5cm^(2)` (Rounded to nearest 1 d.p)