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

Answer 1

To find out how much cardboard Leonard will need for his pyramid, we will use the formula given:

\[ \text{Surface Area} = 4\left(\frac{1}{2} bh\right) + b^2 \]

where \( b \) is the base length and \( h \) is the height of the pyramid.

Given:

• \( b = 3 , \text{in} \)
• \( h = 8 , \text{in} \)

Let's calculate each part of the formula step by step.

First, calculate \( 4\left(\frac{1}{2} bh\right) \):

1. Calculate \( \frac{1}{2} bh \): \[ \frac{1}{2} \times 3 \times 8 = \frac{1}{2} \times 24 = 12 , \text{in}^2 \]

2. Multiply by 4: \[ 4 \times 12 = 48 , \text{in}^2 \]

Next, calculate \( b^2 \): \[ b^2 = 3^2 = 9 , \text{in}^2 \]

Now, combine both parts to find the total surface area: \[ \text{Surface Area} = 48 + 9 = 57 , \text{in}^2 \]

Thus, Leonard will need 57 square inches of cardboard to construct the pyramid.