Question

Art wants to cover both sides of an isosceles triangle with a height of 9 centimeters and a base of 7 centimeters in fabric. How much fabric does he need?
16 cm2
23 cm2
31.5 cm2
63 cm2

Answer 1

To calculate the amount of fabric needed to cover both sides of an isosceles triangle, we first need to find the area of the triangle, and then we can determine the total area of both sides.

1. **Calculate the area of the triangle** using the formula:
\[
\text{Area} = \frac{1}{2} \times \text{base} \times \text{height}
\]

Here, the base \( b = 7 \) cm and the height \( h = 9 \) cm.

\[
\text{Area} = \frac{1}{2} \times 7 \times 9 = \frac{63}{2} = 31.5 \text{ cm}^2
\]

2. **Covering both sides** of the triangle means we need double the area:

\[
\text{Total Fabric Needed} = 2 \times \text{Area} = 2 \times 31.5 = 63 \text{ cm}^2
\]

Therefore, the total amount of fabric Art needs is \( \boxed{63 \text{ cm}^2} \).