Question

All faces of a bench except the two faces that rest on the ground will be coated with a water resistant paint. The bench is a right prism. What is the total area to be coated with paint? Show your work.

Answer 1

Given:

All faces of a bench except the two faces that rest on the ground will be coated with a water-resistant paint.

So, the number of the sides that will be coated = 8 sides

The upper side with dimensions of 63 in and 16 in

Area = 63 * 16 = 1008 in²

Two sides of dimensions of 18.5 in and 16 in

Area = 2 * 18.5 * 16 = 592 in²

Two sides of dimensions of 14 in and 16 in

Area = 2 * 14 * 16 = 448 in²

Two sides on the front and behind, the one side will the difference of total rectangle and the space:

`2(63*18.5-54*14)=819\text{ }in^2`

One side that will face the ground of dimensions 54 in and 16 in

Area = 54 * 16 = 864 in²

So, the total area = 1008 + 592 + 448 + 819 + 864 = 3731 in²

so, the answer will be: Area = 3731 in²