Question

if perimeter of equilateral traingle is 90 m ,find its area?

Answer 1

We know that
Perimeter of equilateral triangle = 3a

90 cm = 3a

90 / 3 = a

a = 30 cm

Now,

We also know that
Area of equilateral triangle

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

Putting the value of a

$= \frac{ \sqrt{3} }{4} \times {(30)}^{2} \\ \\ = \frac{ \sqrt{3} }{4} \times 900 \\ \\ = \sqrt{3} \times 225 \\ \\ = 225 \sqrt{3}$

We know that √3 = 1.732

$= 225 \times 1.732 \\ \\ = 389.7$

So the area of equilateral triangle is 389.7 cm^2

Answer 2

Given ,
perimeter- 90 cm

Let x be the one side of a triangle

First ,
we find the one side of an equilateral triangle is
x+x+x = 90
=> 3x = 90
=> x = 90 ÷ 3
=> x = 30

Therefore , three sides are 30 [ equilateral triangle]
perimeter = 90 cm
Semiperemeter =
$a + b + c\%2$
= 30 + 30 + 30 % 2 = 45 cm

Now ,
we find the area of the triangle

Area=
$\sqrt{s(s - a)(s - b)(s - c)}$
$\sqrt{45(45 - 30)(45 - 30)(45 - 30)}$
$\sqrt{45 \times 15 \times 15 \times 15}$
$\sqrt{3 \times 3 \times 5 \times 3 \times 5 \times 3 \times 5 \times 3 \times 5}$
$\sqrt{ {3}^{2} } \times {3}^{2} \times {5}^{2} \times 3 \times 5$
$3 \times 3 \times 5 \times \sqrt{3 \times 5}$
$45 \sqrt{15}$
$45 \sqrt{15 {cm}^{2} }$
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