Question

Use the L-shaped composite figure formed by two rectangular prisms to answer the question. A 10-inch by 0.5-of-a-foot by 7-inch prism attached to a 10-inch by 1-foot by 4-inch prism. One 10-inch by 0.5of-a-foot face of the top prism covers the same area on the other prism. © 2018 StrongMind What is the surface area of the composite figure in square inches? Enter your answer as a number, like this: 42

Answer 1

The surface area of the composite figure, formed by attaching a 10x0.5x7-inch prism to a 10x1x4-inch prism, is 275 square inches. Calculated by summing the individual prism surface areas.

To find the surface area of the composite figure, calculate the surface area of each prism separately and then add them together.

1. Surface area of the first prism (10 inches by 0.5 feet by 7 inches):

`\[2(10 * 0.5) + 2(10 * 7) + 2(0.5 * 7) = 20 + 140 + 7 = 167 \text{ square inches}\]`

2. Surface area of the second prism (10 inches by 1 foot by 4 inches):

`\[2(10 * 1) + 2(10 * 4) + 2(1 * 4) = 20 + 80 + 8 = 108 \text{ square inches}\]`

3. Total surface area of the composite figure:

`\[167 + 108 = 275 \text{ square inches}\]`

Therefore, the surface area of the composite figure is 275 square inches.