Question
Leonard is going to construct a pyramid with cardboard for math class. Find how many square inches (in.^2) of cardboard he will need. Use 4 (1/2) bh + b2, where b, the base of the pyramid, is 3 in. and h, the height of the pyramid, is 8 in.
Answers
GPT 3.5
To find the surface area of the pyramid, we need to calculate the area of each of the triangular faces and the area of the base.
The formula for the area of a triangle is (1/2)bh, where b is the base of the triangle and h is the height of the triangle.
First, let's find the area of one triangular face. The base (b) is 3 in. and the height (h) is 8 in. So, the area of one triangular face is (1/2)(3)(8) = 12 in^2.
There are four triangular faces, so the total area of the triangular faces is 4(12) = 48 in^2.
Next, let's find the area of the base. The base (b) is 3 in., so the area of the base is (3)(3) = 9 in^2.
Finally, let's find the surface area. The surface area is the sum of the area of the triangular faces and the area of the base. So, the surface area is 48 + 9 = 57 in^2.
Therefore, Leonard will need 57 square inches of cardboard to construct the pyramid.
The formula for the area of a triangle is (1/2)bh, where b is the base of the triangle and h is the height of the triangle.
First, let's find the area of one triangular face. The base (b) is 3 in. and the height (h) is 8 in. So, the area of one triangular face is (1/2)(3)(8) = 12 in^2.
There are four triangular faces, so the total area of the triangular faces is 4(12) = 48 in^2.
Next, let's find the area of the base. The base (b) is 3 in., so the area of the base is (3)(3) = 9 in^2.
Finally, let's find the surface area. The surface area is the sum of the area of the triangular faces and the area of the base. So, the surface area is 48 + 9 = 57 in^2.
Therefore, Leonard will need 57 square inches of cardboard to construct the pyramid.