The figure below is a net for a triangular prism. Side a = 46 inches, side b = 10 inches, side c = 31 inches, and altitude d = 21 inches. What is the surface area of this figure?

Answer 1

We can start by breaking down the figure into its three rectangular faces and two triangular faces.

The rectangular faces have dimensions 46 x 21, 10 x 21, and 31 x 21.
The triangular faces have base 46, 10, and 31, with a height of 21.

To find the area of a triangle with base b and height h, we use the formula A = (1/2)bh.

So the area of the triangular faces are:

- (1/2)(46)(21) = 483 square inches
- (1/2)(10)(21) = 105 square inches
- (1/2)(31)(21) = 325.5 square inches

To find the area of a rectangle with length l and width w, we use the formula A = lw.

So the area of the rectangular faces are:

- 46 x 21 = 966 square inches
- 10 x 21 = 210 square inches
- 31 x 21 = 651 square inches

Adding up all the areas, we get:

483 + 105 + 325.5 + 966 + 210 + 651 = 2740.5

Therefore, the surface area of the triangular prism is approximately 2740.5 square inches.