Name: Area of a Triangle by Heron's Formula
Uploaded: 2019-07-19
Duration: 7 min 5 s
Description: Do you know how to calculate the area of a triangle when all three side lengths are given? It is very easy. Watch this video to understand how to calculate.

Question

A traffic signal board, indicating

‘ S C H O O L A H E A D ’

, is an equilateral triangle with side

‘ a ’ .

Find the area of the signal board, using Heron’s formula. If its perimeter is

180 c m,

what will be the area of the signal board?

Accepted Answer

Given,

The length of one side of a traffic signal board $= a c m$

We know that the perimeter of an equilateral triangle $= 3 \times side$

Hence, the perimeter of the traffic signal board $= 3 a c m$

And, the semi-perimeter of the traffic signal board, $s = \frac{3 a}{2} c m$

We know that according to Heron’s Formula,

Area of the triangle $= \sqrt{s (s - a) (s - b) (s - c)}$ ,

where $s$ is the semi-perimeter and $a, b, c$ are the length of the sides.

So, the area of traffic signal board is,

$= \sqrt{\frac{3 a}{2} (\frac{3 a}{2} - a) (\frac{3 a}{2} - a) (\frac{3 a}{2} - a)}$

$= \sqrt{\frac{3 a}{2} \times \frac{a}{2} \times \frac{a}{2} \times \frac{a}{2}}$

$= \frac{\sqrt{3} a^{2}}{4} c m^{2}$

Given,

The perimeter of the signal board $= 180 c m$

$\Rightarrow 180 = 3 a$

$\Rightarrow a = 60 c m$

Hence, the area of traffic signal board is,

$= \frac{\sqrt{3} a^{2}}{4}$

$= \frac{\sqrt{3}}{4} \times 60^{2} {cm}^{2}$

$= \sqrt{3} \times 900 c m^{2}$

$= 900 \sqrt{3} c m^{2}$

Thus, the area of the signal board is $900 \sqrt{3} c m^{2}$

A traffic signal board, indicating $‘ S C H O O L A H E A D ’$ , is an equilateral triangle with side $‘ a ’ .$ Find the area of the signal board, using Heron’s formula. If its perimeter is $180 c m,$ what will be the area of the signal board?

Important Questions on Heron's Formula

Learn and Prepare for any exam you want !

A traffic signal board, indicating ‘SCHOOL AHEAD’, is an equilateral triangle with side ‘a’. Find the area of the signal board, using Heron’s formula. If its perimeter is 180 cm, what will be the area of the signal board?

Important Questions on Heron's Formula

Learn and Prepare for any exam you want !

A traffic signal board, indicating $‘ S C H O O L A H E A D ’$ , is an equilateral triangle with side $‘ a ’ .$ Find the area of the signal board, using Heron’s formula. If its perimeter is $180 c m,$ what will be the area of the signal board?