Question

if the perimeter of an equilateral triangle is 36 cm ,calculate its area and height correct to one decimal place...

Answer 1

perimeter of the triangle is the sum of the lengths of all sides. Since, this is an equilateral triangle, lengths of all sides are equal. Therefore, length of one side will be:

36/3 = 12cm

We can find the height using Pythagoras' Theorem, by diving the triangle into two equal halbes, such that a right angle is formed.

This way you'll have a 12cm tilted side (hypotenuse), a 6cm adjacent, and an unknown opposite, which is the height (h).

h^2 = 12^2 - 6^2
h = 10.4cm

Then you can find out the area using this height.

Area= 1/2 × base × height
= 1/2 × 6 × 10.4
= 31.2cm^2

Answer 2

hey here is your answer.

Given perimeter of equilateral triangle = 36 cm

Let the side of equilateral triangle be 'a' cm

Hence 3a = 36

Therefore, a = 12 cm



Area of equilateral triangle = (√3/4) x a2 sq units
= (√3/4) x 122
= (√3/4) x 144 = 36√3 sq cm
= 62.3 sq cm

I hope it will help you..