Question

Calculate the area of the shaded part to 1dp​

Answer 1

To find the area of the shaded region

A = Area of circle - Area of square

12cm is the diagonal of the square and diameter of the circle.

To find the side of the square,

d = √2 * s

12cm = √2 * s

s = 8.49cm

Area of square = L²

As = (8.49)²

As = 72.1cm²

Area of circle = πr²

r = 6cm

Ac = (π*36)cm²

Ac = 113.1cm²

A = Ac - As

A = 113.1cm² - 72.1cm²

A = 41cm²

The area of the shaded region is 41cm².

Answer 2

Answer: I can't tell from the photo which is the shaded part. I'll answer on the assumption it is either the square in the circle, or the 4 areas defined by the semicircles outside the square, but inside the circle.

Step-by-step explanation: Note the caveat above.

Circle Area = pi*r^2 or (3.14)*(6cm)^2 = 113.1 cm^2

Area of the square: The 12cm line forms an hypotenuse with either side. The sides are all equal, so if x is 1 side, we can say the area is x^2. We also know tha x^2 + x^2 = 12

x^2 = 6 cm^2 (the area of the square)

The two possible answers:

1) Shaded portion is the square: 6 cm^2

2) Shaded area means the 4 semicircles outside the square but within the circle: 113.1 cm^2 - 6 cm^2 = 107.1 cm^2