The area of the incircle of an equilateral triangle is 49π cm2. Find

1.	The area of the incircle of an equilateral triangle is 49π cm2. Find the area of its circumcircle.1. 196π cm22. 192π cm23. 49π cm24. 169π cm2
Answer» Correct Answer - Option 1 : 196π cm² Given: The area of the incircle of an equilateral triangle is 49π cm². Formula used: Inradius of equilateral triangle = a/(2√3) Circumradius of equilateral triangle = a/(√3) Where, a = side of an equilateral triangle Calculation: Inradius of equilateral triangle = a/(2√3) Area of incircle = π(a/2√3)² ⇒ π(a/2√3)² = 49π ⇒ (a²)/12 = 49 ⇒ a² = 49 × 12 ⇒ a = 14√3 Circumradius of equilateral triangle = a/√3 ⇒ (14√3)/√3 ⇒ 14 Area of Circumcircle ⇒ π(14)² ⇒ 196π cm² ∴ Area of Circumcircle is 196π cm².

The area of the incircle of an equilateral triangle is 49π cm2. Find the area of its circumcircle.1. 196π cm22. 192π cm23. 49π cm24. 169π cm2

Answer» Correct Answer - Option 1 : 196π cm²

Given:

The area of the incircle of an equilateral triangle is 49π cm².

Formula used:

Inradius of equilateral triangle = a/(2√3)

Circumradius of equilateral triangle = a/(√3)

Where,

a = side of an equilateral triangle

Calculation:

Inradius of equilateral triangle = a/(2√3)

Area of incircle = π(a/2√3)²

⇒ π(a/2√3)² = 49π

⇒ (a²)/12 = 49

⇒ a² = 49 × 12

⇒ a = 14√3

Circumradius of equilateral triangle = a/√3

⇒ (14√3)/√3

⇒ 14

Area of Circumcircle

⇒ π(14)²

⇒ 196π cm²

∴ Area of Circumcircle is 196π cm².