To find the surface area of the pyramid using the formula you provided, we need to substitute in the values for the base \( b \) and the height \( h \).
Given:
- Base width \( b = 3 \) inches
- Height \( h = 8 \) inches
The formula given is:
\[ 4(1/2)bh + b^2 \]
Let's break it down:
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Calculate \( 4(1/2)bh \): \[ 4(1/2)bh = 4 \times \frac{1}{2} \times 3 \times 8 = 2 \times 3 \times 8 = 48 , \text{in}^2 \]
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Calculate \( b^2 \): \[ b^2 = 3^2 = 9 , \text{in}^2 \]
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Now, add both parts together: \[ \text{Total Surface Area} = 48 + 9 = 57 , \text{in}^2 \]
Thus, Leonard will need 57 square inches of cardboard to construct the pyramid.