A regular hexagon is inscribed in a circle. If the area of hexagon is 24√3 cm², find the area of the circle. (Use π = 3.14)
Answers
Answer:
The area of circle is 50.24 cm²
Step-by-step explanation:
Let ‘r’ be the radius of a circle and ‘a’ be the side of a hexagon.
Given :
Area of hexagon = 24√3 cm²
Area of hexagon = 3√3/2 a²
24√3 = 3√3/2 a²
24 × 2 = 3a²
48 = 3a²
a² = 48/3
a² = 16
a = √16
a = 4 cm
Side of a hexagon = 4 cm
Radius of circle,r = Side of a hexagon = 4 cm
[In regular hexagon inscribed in a circle, its side is equal to the radius of a Circle]
Radius of circle,r = 4 cm
Area of circle,A = πr²
A = 3.14 × 4²
A = 3.14 × 16
A = 50.24 cm²
Area of circle = 50.24 cm²
Hence, the area of circle is 50.24 cm²
HOPE THIS ANSWER WILL HELP YOU….
dividing a hexagon into 6 equal parts give 6 triangles with angle at center being 360/6 =60 degrees.
Area of hexagon =6 x area of each triangle.
Area of triangle = 1/2 ab sin Ѳ(where Ѳ= angle b/w the sides)
ĺa" and "b" are both= "r" = the radius of the circle.
area of hexagon =6 x 1/2 x r x rx sin 60 = 24√3
r^2 = 16
r=4cm
area of circle = 22/7 x 4^2 = 50.29 cm^2.
✌✌✌✌✌✌✌✌