Jesse found a set of new erasers that are shaped like right triangular prisms which is his favorite three dimensional shape. After some quick measurements, he 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 hypot0of 5 inches. Furthermore, the eraser is 6.25 inches long. Using a net,figure out the total surface area of the eraser.

Answer 1

To find the total surface area of the eraser, we first need to find the surface area of each triangular face and the surface area of the three rectangular faces.

The formula for the surface area of a triangular prism includes the area of the two triangular faces and the areas of the three rectangular faces:

Surface Area = 2(base * height of triangle) + (perimeter of triangle * height of prism)

First, let's find the area of one triangular face:
Area of triangle = (1/2) * base * height
Area of triangle = (1/2) * 4 * 3
Area of triangle = 6 square inches

The total area of the two triangular faces is 2 * 6 = 12 square inches.

Next, let's find the perimeter of the triangle:
Perimeter of triangle = a + b + c
Perimeter of triangle = 4 + 3 + 5
Perimeter of triangle = 12 inches

Now, let's find the area of one rectangular face:
Area of rectangle = length * width
Area of rectangle = 6.25 * 3
Area of rectangle = 18.75 square inches

The total area of the three rectangular faces is 3 * 18.75 = 56.25 square inches

Now, let's calculate the total surface area of the eraser:
Surface Area = 12 + 56.25
Surface Area = 68.25 square inches

Therefore, the total surface area of the eraser is 68.25 square inches.