Question

Calculate the area of the shaded region in each figure. Use 3.14 and round to the nearest tenth, if necessary.

Answer 1

Given:

Given that the length of the side of the square is 12 cm.

The given figure consists of two circles with radius of 3 cm each.

We need to determine the area of the shaded region.

Area of the square:

The area of the square can be determined using the formula,

`A=s^2`

Substituting s = 12, we get;

`A=12^2`

`A=144 \ cm^2`

Thus, the area of the square is 144 square cm.

Area of the two circles:

The area of the circle can be determined using the formula,

`A=\pi r^2`

Substituting r = 3, we get;

`A=(3.14)(3)^2`

`A=(3.14)(9)`

`A=28.26 \ cm^2`

The area of 2 circles is given by

`A=2(28.26)`

`A=56.52 \ cm^2`

Thus, the area of the two circles is 56.52 square cm.

Area of the shaded region:

The area of the shaded region can be determined by subtracting the area of the two circles from the area of the square.

Thus, we have;

Area = Area of square - Area of two circles.

Substituting the values, we get;

`Area = 144- 56.52`

`Area=87.5 \ cm^2`

Thus, the area of the shaded region is 87.5 square cm.