Question

lila made a triangular flag to cheer on her favorite sports team. the perimeter of the flag is 20 inches. approximately how many square inches of fabric were used to make the triangular flag? 15 square inches 76 square inches 186 square inches 215 square inches heron’s formula: area = √s(s - a)(s - b)(s - c)

Explanation:

Step1: Find the third side length

The perimeter of a triangle is the sum of its three sides. Given two sides are 8 in and 8 in, and the perimeter is 20 in. Let the third side be \( c \). So, \( 8 + 8 + c = 20 \). Solving for \( c \), we get \( c = 20 - 16 = 4 \) in.

Step2: Calculate the semi - perimeter (\( s \))

The semi - perimeter \( s=\frac{a + b + c}{2}\), where \( a = 8 \), \( b = 8 \), \( c = 4 \). So, \( s=\frac{8 + 8+4}{2}=\frac{20}{2}=10 \) in.

Step3: Apply Heron's formula

Heron's formula is \( \text{Area}=\sqrt{s(s - a)(s - b)(s - c)} \). Substituting \( s = 10 \), \( a = 8 \), \( b = 8 \), \( c = 4 \) into the formula:
\( \text{Area}=\sqrt{10(10 - 8)(10 - 8)(10 - 4)}=\sqrt{10\times2\times2\times6}=\sqrt{240}\approx15.49\approx15 \) square inches.

Answer:

15 square inches