Question

5. Find the area of the shaded

region. Round to the nearest
tenth where necessary
(1 decimal places).
A=
12 cm

Answer 1

Area_shaded

= 82.2 cm^2

Explanation:

Here's the plan: Find the area of the circle and subtract the area of the square.

The area of the square is:

Area_square= s^2

OR just length×width.

We are given the side. So the area is

Area_square

= 12^2 = 12×12

= 144

The Area_circle

= pi•r^2

So now we need to find r, the radius of the circle.

The diagonal of the square is the diameter of the circle. We can find the diagonal (Pythagorean Thm or Special Right Triangles 45°-45°-90°) and cut it in half to find the radius.

See image.

The diagonal which is the diameter is 12root2. So the radius is 6root2.

r = 6root2

Area_circle

= pi•(6root2)^2

= pi•72

= 72pi

~= 226.194671

Subtract.

Area_circle - Area_square

= 226.194671 - 144

= 82.194671

round to nearest tenth (one decimal place)

~= 82.2 cm^2

see image