To determine the amount of cardboard Leonard will need to construct the pyramid, we use the given formula:
\[ 4 \left( \frac{1}{2} \right) b h + b^2 \]
Let's break down the steps to solve this:
1. **Substitute the given values**: Base \( b = 3 \) inches and height \( h = 8 \) inches.
2. **Calculate the term \( 4 \left( \frac{1}{2} \right) b h \)**:
\[ 4 \left( \frac{1}{2} \right) \times 3 \times 8 \]
Step-by-step:
- Calculate \( \frac{1}{2} \times 3 \):
\[ \frac{1}{2} \times 3 = 1.5 \]
- Multiply 1.5 by 8:
\[ 1.5 \times 8 = 12 \]
- Multiply by 4:
\[ 12 \times 4 = 48 \]
3. **Calculate the term \( b^2 \)**:
\[ 3^2 = 9 \]
4. **Add these results together**:
\[ 48 + 9 = 57 \]
So, Leonard will need 57 square inches of cardboard to construct the pyramid.
\[ \boxed{57 \text{ in}^2} \]
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) in.2
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