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 herons formula area = √s(s - a)(s - b)(s - c)

Explanation:

Step1: Find the semi - perimeter

The perimeter $P = 20$ inches. The semi - perimeter $s=\frac{P}{2}=\frac{20}{2}=10$ inches.

Step2: Assume the side lengths

Let two sides $a = 8$ inches and $b = 8$ inches. Then the third side $c=20-(8 + 8)=4$ inches.

Step3: Apply Heron's formula

Area $A=\sqrt{s(s - a)(s - b)(s - c)}=\sqrt{10(10 - 8)(10 - 8)(10 - 4)}=\sqrt{10\times2\times2\times6}=\sqrt{240}\approx15.5$ square inches.

Answer:

15 square inches