Question

An equilateral triangle is inscribed in a circle of radius 7 cm. Find the area of the triangle​

Answer 1

Answer:

147 √3 / 4   cm²

63.65 cm²

Step-by-step explanation:

An equilateral triangle is inscribed in a circle of radius 7 cm. Find the area of the triangle​

Let say ABC is Equilateral Trinagle

O is the center point

then  OA = OB = OC + radius = 7 cm

in Δ OAB

OA = OB = 7cm  AB = >

∠AOB = 360°/3 = 120°

AB² = OA² + OB² - 2ABCos∠AOB

=> AB² = 7² + 7² - 2*7*7Cos120°

=> AB² = 98 - 98(-1/2)

=> AB² = 98 + 49

=> AB² = 147

=> AB = 7√3

ABC is equilateral triangle

AB = BC = CA = 7√3

Area of equilateral Triangle = (√3 / 4) Side²

= (√3 / 4) (7√3)²

= 147 √3 / 4

= 63.65 cm²