Question

perimeter of an equilateral triangle is 30m, find its area?




Please help guys.......!!​

Answer 1

Answer:

The area of the equilateral triangle is 50m .

Step-by-step explanation:

Given :

Perimeter of the equilateral triangle = 30 m

To find :

The area of the equilateral triangle

Concept :

So , in equilateral triangle all sides are same . So , to find the area of the equilateral triangle we have to first find the length of one side of the equilateral triangle.

And to find the one side of the equilateral triangle use this formula -:

$\boxed{\sf{S=\dfrac{P}{3}}}$

Where,

S = Length of one side of the equilateral triangle

P = Perimeter of the equilateral triangle

So , after find the length of one side of the equilateral triangle . To find the area of the triangle use this formula -:

$\boxed{\sf{A=\dfrac{H\:\times\:B}{2}}}$

Where,

A = Area of the triangle

H = Height

B = Base

Solution :

Length of one side of the equilateral triangle -:

$\leadsto\sf{S=\dfrac{\cancel{30}m}{\cancel{3}}}$

$\leadsto\sf{S=10m}$

So , the length of one side of the equilateral triangle is 10 m .

And the all sides of the equilateral triangle is same . So , its Height and Base is also same .

Area of the equilateral triangle -:

$\leadsto\sf{A=\dfrac{10m\times10m}{2}}$

$\leadsto\sf{A=\dfrac{\cancel{100}m}{\cancel{2}}}$

$\leadsto\sf{A=50m}$

So , the area of the equilateral triangle is 50 m .

Answer 2

Answer:

In an equilateral triangle all the sides are equal.

therefore the length of one of the sides is 30/3 = 10m.

By heron's formula, we can find the area of a traiangle if we know all the three sides.

area of a traingle = root of s*(s-a) *(s-b) *(s-c)

• here s = a+b+c/2

• a, b, and c are the three sides of triangle.

• here a, b and c is 10m

s= 10+10+10/2

= 30/2

= 15

area of the traingle =

$\sqrt{15 \times (15 - 10) \times (15 - 10) \times (15 - 10)}$

$= \sqrt{15 \times 5 \times 5 \times 5}$

$= \sqrt{45 \times {5}^{3} }$

$= 5 \times \sqrt{45 \times 5}$

{as 5^3 can be splitted into 5^2 * 5

so from here we can take one five from the first term and that term will be cancelled.}

$= 5 \times \sqrt{225}$

$= 75$

(root 225 = 15)

this is the answer.