Question

the semi perimeter of an equilateral triangle is 60cm. find the area

Answer 1

3a/2= 60
3a = 120
a= 40
area= √3 /2 à²= 800√3 cm ² will be the answer

Answer 2

Answer:

The area is 400√3 square cm.

Step-by-step explanation:

Given,semi perimeter of an equilateral triangle is 60cm.

Semi perimeter means half of perimeter.

Semi perimeter means half of perimeter.We know perimeter of a triangle is sum of all sides of the triangle.

Let all sides of an equilateral triangle be a unit

Then perimeter of the triangle is $a + a + a = 3a$unit.

Now semi perimeter of the triangle is = half of the perimeter $= \frac{3a}{2}$

According to question,

$\frac{3a}{2} = 60$

By cross multiplication,

$3a = 60 \times 2 \\ a = \frac{60 \times 2}{3} \\ a = 20 \times 2 \\ a= 40$

So,side of the triangle is 40 cm.

Now we want to find Area.

We know area of equilateral triangle is $\frac{ \sqrt{3} }{4} {a}^{2}$

where a is side of triangle.

So, area of the given triangle is

$\frac{ \sqrt{3} }{4} \times {40}^{2} \\ = \frac{ \sqrt{3} }{4} \times 40 \times 40 \\ = \sqrt{3} \times 10 \times 40 \\ = 400 \sqrt{3}$square cm.