A carpenter is building a unique jewelry box in the shape of a right triangular prism. The base has measurements of 4 inches, 3 inches, and 5 inches. How much wood will it take to complete the project if it is 6 inches tall?

Answer: The carpenter will need 84 square inches of wood.

In this problem we are looking for the surface area of the jewelry box. This box has 5 faces. The two triangles at each end and the 3 rectangle pieces between them.

The sides of the triangles are 3, 4, 5 which always forms a right triangle with legs of 3 and 4. Use the formula for the area of a triangle, we have 3 x 4 / 2 = 6. The area of each triangle is 6 square inches.

Now, the three sides, each one has a height of 6.

3 x 6 = 18

4 x 6 = 24

5 x 6 = 30

If we add all the sides together, we get an area of 84 square inches.

6 + 6 + 18 + 24 + 30 = 84