Question

4. If perimeter of an equilateral triangle is equal to its area, find
the area of triangle.​

Answer 1

Given,

If perimeter of an equilateral triangle is equal to its area

To find,

Find  the area of triangle.​

Solution :

Let each side of equilateral triangle be 'a' unit

∴ Perimeter of equilateral Δ = 3a unit

∴ Area of equilateral Δ = √3/4 a² unit²

Now atq,

$\longmapsto\sf 3a = \dfrac{ \sqrt{3}} {4} \ a^2 \\\\ \\ \longmapsto\sf 3 = \dfrac{ \sqrt{3}}{4} \ a \\\\ \\ \longmapsto\sf 12 = \sqrt{3} a \\\\ \\ \longmapsto\sf a = \dfrac{12}{\sqrt{3}} \\\\ \\ \longmapsto\sf a = \dfrac{4 \times \sqrt{3} \times \sqrt{3} }{\sqrt{3}} \\\\ \\ \longmapsto\bold{a = 4\sqrt{3} \ unit }$

Now area of equilateral Δ :

$\longmapsto\sf Area_{\triangle} = \dfrac{\sqrt{3}}{4} \times {(4 \sqrt{3})}^2 \\\\ \\ \longmapsto\sf Area_{\triangle} = \dfrac{\sqrt{3}} {4} \times 48 \\\\ \\ \longmapsto\bold{Area_{\triangle} = 12\sqrt{3} \ unit^2 }$

Therefore,

Area of equilateral triangle = 12√3 unit²

Answer 2

Given :

➝ Perimeter of an equilateral triangle is equal to its area.

To find :

➝ Area of equilateral triangle.

Formula used :

➝Area of equilateral triangle = (√3/4) a²

➝Perimeter of equilateral triangle = 3a

Where :- a = length of each side of equilateral triangle

Solution :

It is given that :- Perimeter of an equilateral triangle is equal to its area.

➝ 3 a ×4 = √3a²

➝ 12a = √3a²

➝ √3a= 12

➝ a= 12/√3

➝ a= (12/√3 ) × ( √3 / √3 )

➝ a= 4√3 units

Area of equilateral triangle = (√3/4) a²

➝ (√3/4) (4√3 )²

➝ 12 √3

➝ 12 √3 square unit

Answer :

➝ 12 √3 square units

Additional-Information :

➝ Area of circle = π r²

➝ Area of square = (side)²

➝ Area of rectangle = length × breath

➝ Circumference of circle = 2πr

➝ Perimeter of square = 4 × side

➝ Perimeter of rectangle = 2( length+breadth)

➝ Perimeter of any figure = sum of all sides of that figure