Question

Please help me solve this

Answer 1

Based on the diagram shown above, the area of the shaded region in terms of π is 432 - 54π square inches.

In Mathematics and Geometry, the area of a rectangle can be calculated by using the following mathematical equation:

Area of rectangle = length × width

By substituting the given side lengths into the formula for the area of a rectangle, we have the following;

Area of rectangle = 18 × (6 + 12 + 6)

Area of rectangle = 432 square inches.

In Mathematics and Geometry, the area of a circle with radius (r) can be calculated by using this formula:

Area of circle = π
`r^2`

Area of circle = π ×
`((6)/(2) )^2`

Area of circle = 9π square inches.

Area of circle = π ×
`((12)/(2) )^2`

Area of circle = 36π square inches.

Area of circle = π ×
`((6)/(2) )^2`

Area of circle = 9π square inches.

Now, we can determine the area of the shaded region as follows;

Area of the shaded region = 432 - 9π - 9π - 36π

Area of the shaded region = 432 - 54π square inches.