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(12)bh+b2 , where b , the base of the pyramid, is 3 in. and h , the height of the pyramid, is 8 in.(1 point)
To find the amount of cardboard Leonard will need, we can use the formula given:
Area = 4(12)bh + b^2
In the given formula, b represents the base of the pyramid, and h represents the height of the pyramid. Plugging in the values for b and h:
b = 3 inches
h = 8 inches
We can calculate the area:
Area = 4(1/2)(3 inches)(8 inches) + (3 inches)^2
First, calculate the area of one triangular face:
Area of one triangle = 1/2 * base * height
= 1/2 * 3 inches * 8 inches
= 1.5 inches * 8 inches
= 12 square inches
Now, since there are four triangular faces, we multiply this area by 4:
Area of four triangles = 4 * 12 square inches
= 48 square inches
Next, calculate the area of the square base:
Area of base = base * base
= 3 inches * 3 inches
= 9 square inches
Now, add the area of the four triangles and the base to get the total area:
Total area = area of four triangles + area of base
= 48 square inches + 9 square inches
= 57 square inches
Hence, Leonard will need 57 square inches of cardboard to construct the pyramid.