Question

Kim bought a jewelry box. She wants to paint all of the exterior faces of the jewelry box. How much paint does she need? Solve on paper, then enter your answer on Zearn. You can use the calculator to help you solve. Right trapezoidal prism with side lengths labeled 3 in, 11 in, 6 in, 5 in and 7 in. Kim's jewelry box

Answer 1

Answer: 0.7523 sq ft

Explanation:

To determine the amount of paint Kim will need, we need to find the surface area of the interior of the box. We can do this by subtracting the surface area of the top and bottom faces (base and lid) from the total surface area of the 4 vertical faces.

Let's start by finding the surface area of the top and bottom faces. We can do this by finding the area of the base (11 in) by the height of the box (6 in) and then multiply it by 2 because there are two bases (top and bottom):

SA (top and bottom) = (base * height) * 2 = (11 in * 6 in) * 2 = 132 in^2

Next, we find the surface area of the 4 vertical faces:

SA (4 faces) = (2 * 3 in * 5 in) + (2 * 4 in * 6 in) + (2 * 3 in * 7 in) = 84 in^2

Finally, we subtract the surface area of the top and bottom faces from the surface area of the 4 vertical faces to find the amount of paint Kim needs:

SA (paint) = (84 in^2) - (132 in^2) = (1/2) * (84 in^2)

= 126 in^2

The amount of paint Kim needs is 126 square inches or 0.7523 square feet.