Question

18.
If the perimeter of an equilateral triangle is 60 cm, then what is its area?
a) 200 V2cm2
b) 100 V2cm2 10013cm
d) 20013cm2​

Answer 1

$\Large{\underbrace{\underline{\sf{Understanding\; the\; Question}}}}$

Here in this question, concept of perimeter as well as area of equilateral triangle is used. We are given perimeter of equilateral triangle and we have to find area of triangle. We know that sides of equilateral triangle are equal. To find area, we have to first find the length of equilateral triangle.

So let's start!!

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Perimeter of equilateral triangle can be defined as sum of all sides of 3 multiply by its side.

Let us assume side of triangle be x.

Perimeter of equilateral triangle=Sum of all sides

60cm=x + x + x

60cm=3x

Now divide 3 from both sides.

60cm÷3=3x÷3

20cm=x

So length of each side of equilateral triangle is 20cm.

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Now we have formula for area of equilateral triangle:

$\sf Area\: of\: equilateral\:\triangle=\dfrac{\sqrt3}{4}\times Side^2$

Now put the value of length of side.

$\sf Area\: of\: equilateral\:\triangle=\dfrac{\sqrt3}{4}\times (20cm)^2$

$\sf Area\: of\: equilateral\:\triangle=\dfrac{\sqrt3}{4}\times 400cm^2$

$\sf Area\: of\: equilateral\:\triangle=\sqrt3\times 100cm^2$

$\sf Area\: of\: equilateral\:\triangle=100\sqrt3\:cm^2$

So the required area of equilateral triangle is 100√3 cm².

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