Question

The diagram shows a square ABCD with sides of length 20cm. it also shows a semi circle and an arc circle AB is the diameter of the semi circle BD is an arc of a circle with the centre A. Find the area of the shaded region giving your answer in terms of pie. you must show your working, clearly stating the area of the semi circle.

I got 1 out of 4 Marks for pie/8 which equalled the shaded region over the area of the square but I have no clue for the area of the semi circle​

Answer 1

Area of Shaded Region
`=50\pi$ cm^2`

Area of Semicircle
`=50\pi$ cm^2`

`\frac{\text{Area of Shaded region}}{\text{Area of Square}}=( \pi)/(8)`

Explanation:

Area of Shaded Region = Area of Sector - Area of Semicircle

Area of Sector

Radius of the sector =20cm

`=(90)/(360)X\pi *20^2\\ =100\pi cm^2`

Area of Semicircle

Since AB is the diameter of the semicircle

Radius of the Semicircle=20/2=10cm

Area of semicircle

`=(\pi r^2)/(2)\\ =(\pi *10^2)/(2)\\=50\pi cm^2`

Therefore, area of Shaded Region

`=100\pi -50 \pi\\=50\pi$ cm^2`

Area of Square =20 X 20
`=400 cm^2`

`\frac{\text{Area of Shaded region}}{\text{Area of Square}} \\=(50 \pi)/(400) \\=( \pi)/(8)`