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 a 4 in, a height of 3 in, and a hypotenuse a 5 in. Furthermore, the eraser is 6.25 inches long. Using a net, figure out the total surface area of the eraser
To find the total surface area of the eraser, we first need to find the surface area of each triangle on the ends and the surface area of the rectangular faces.
Surface area of each triangle:
Since the shape is a right-angled triangle, we can use the formula:
Surface area = 0.5 * base * height
Surface area = 0.5 * 4 in * 3 in = 6 in^2
There are two triangular faces on the eraser, so the total surface area of the triangular faces is 2 * 6 in^2 = 12 in^2
Surface area of the rectangular faces:
The rectangular faces are the sides of the prism, so we need to find the dimensions of the rectangle formed by unwrapping the prism.
The dimensions of the rectangle will be:
Length = 6.25 in
Width = 5 in (hypotenuse of the triangle)
Surface area of each rectangular face:
Surface area = length * width
Surface area = 6.25 in * 5 in = 31.25 in^2
There are four rectangular faces on the eraser, so the total surface area of the rectangular faces is 4 * 31.25 in^2 = 125 in^2
Total surface area of the eraser:
Total surface area = surface area of triangular faces + surface area of rectangular faces
Total surface area = 12 in^2 + 125 in^2 = 137 in^2
Therefore, the total surface area of Jesse's favorite right angled triangular prism eraser is 137 square inches.