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)
To find the total surface area of the eraser, we need to calculate the area of each of the five faces and then add them up.
First, let's calculate the area of the two triangular faces:
Area = (1/2) * base * height
= (1/2) * 4 * 3
= 6 square inches
Since there are two triangular faces, the total area of the triangular faces is 2 * 6 = 12 square inches.
Next, let's calculate the area of the three rectangular faces:
Area = length * width
There are two rectangular faces with dimensions 6.25 (length) and 3 (width):
Area = 6.25 * 3
= 18.75 square inches
There is also a rectangular face with dimensions 6.25 (length) and 4 (width):
Area = 6.25 * 4
= 25 square inches
Adding up the areas of all five faces:
Total Surface Area = 12 + 18.75 + 25
= 55.75 square inches
Therefore, the total surface area of the eraser is 55.75 square inches.