Jesse found a set of new erasers that are shaped like right angled triangular prisms, which is his favorite three-dimensional shape. After some quick measurements, he has figured out that the sides of the triangle on each end of the eraser have a base of 4 inches, a height of 3 inches, and a hypotenuse of 5 inches. Furthermore, the eraser is 6.25 inches long. Using a net, figure out the total surface area of the eraser. (1 point)

Question

____in.2

Answer 1

To find the total surface area of the eraser, we need to calculate the area of each of the five faces and then sum them up.

1. The two triangular faces:
Each triangular face has an area of (1/2) * base * height
= (1/2) * 4 * 3
= 6 in^2
Since there are two triangular faces, the total area of both is 2 * 6 = 12 in^2

2. The three rectangular faces:
Each rectangular face has an area of base * height
= 4 * 6.25
= 25 in^2
Since there are three rectangular faces, the total area of all three is 3 * 25 = 75 in^2

Now, summing up the areas of all five faces:
12 + 75 = 87 in^2

Therefore, the total surface area of the eraser is 87 square inches.