Question

The perimeter of equilateral triangle is 21m. Find the area. Using Heron's Formula

Answer 1

Answer:

A ≈ 21.22 m²

Step-by-step explanation:

The area (A) of a triangle using Heron's formula is

A = $\sqrt{s(s-a)(s-b)(s-c)}$

where s is the semi perimeter and a, b, c the sides of the triangle.

Here the perimeter of the equilateral triangle is 21 m , then

a = b = c = 21 ÷ 3 = 7 m

s = 21 ÷ 2 = 10.5

Then

A = $\sqrt{10.5(10.5-7)(10.5-7)(10.5-7)}$

   = $\sqrt{10.5(3.5)(3.5)(3.5)}$

   = $\sqrt{450.1875}$

   ≈ 21.22 m² ( to 2 dec. places )