To find the total surface area of the eraser, we need to calculate the surface area of each of the six faces of the triangular prism.
1. Base:
The base of the triangular prism is a right-angled triangle with a base of 4 inches and a height of 3 inches. The area of this triangle can be calculated as:
Area = 1/2 * base * height
Area = 1/2 * 4 * 3
Area = 6 square inches
Since there are two bases on the eraser, the total area of the bases is 2 * 6 = 12 square inches.
2. Sides:
Each side of the eraser is a rectangle with dimensions of 6.25 inches (length) and 4 inches (height). The area of each side can be calculated as:
Area = length * height
Area = 6.25 * 4
Area = 25 square inches
Since there are three sides on the eraser, the total area of the sides is 3 * 25 = 75 square inches.
Therefore, the total surface area of the eraser is the sum of the areas of the bases and the sides:
Total surface area = 12 (bases) + 75 (sides)
Total surface area = 87 square inches
Therefore, the total surface area of the eraser is 87 square inches.
Jesse found a set of new erasers that are shaped like right angled triangular prisms. After some quick measurements, he has figured out that the sides of the triangle of 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.
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