Problem:

A square has an area of 9 sq.m and has a perimeter which is equal to the perimeter of an equilateral triangle. What is the area of the equilateral triangle?​

Solution:

Area = 9 sqm

P = same as an equilateral triangle

Area of square = s²

side of square = 3 m

Perimeter of square = 3 + 3 + 3 + 3

Perimeter of square = 12 m

Perimeter of square = Perimeter of equilateral triangle

To get the height,

use the Pythagorean theorem

4² = 2² + h²

16 - 4 = h²

h² = 12

h = √12

h = 3.46

Area of equilateral triangle = 1/2(4)(h)

Area of equilateral triangle = 1/2(4)(√12)

Area of equilateral triangle = 6.92820323028

Answer:

Area of equilateral triangle = 6.928 sqm

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