PQRSTV is a regular polygon of side 7 cm inscribed in a circle. Find the circumference of the circle PQRSTV.
A.
56 cm
B.
22 cm
C.
42 cm
D.
44 cm
Correct Answer: 44 cm
Explanation
Each interior Angle of the polygon = (n-2) 180
_n
= (6-2) 180
_6
= 4 x 30
= 120°
i.e ∠PQR = 120° ∴ RQD = 120/2 = 60° also
∴ Δ QOR is equilateral Δ ∴ QO = 7cm
∴ PO = QO = RO ...... = 7cm radius of the circumference of the circle = 2πr
= 2 x 22/7 x 7/1
= 44 cm
Each interior Angle of the polygon = (n-2) 180
_n
= (6-2) 180
_6
= 4 x 30
= 120°
i.e ∠PQR = 120° ∴ RQD = 120/2 = 60° also
∴ Δ QOR is equilateral Δ ∴ QO = 7cm
∴ PO = QO = RO ...... = 7cm radius of the circumference of the circle = 2πr
= 2 x 22/7 x 7/1
= 44 cm