In the given figure AOB is a sector of angle 60 degree of a circle with Centre O and radius 17 cm if AP is perpendicular to OB and AP=15 cm find the area of shaded portion.
Answers
Answer:
Area of sector OAB = 60 ÷ 360 × π×r²
Here r =17 = 22× 17²÷ 42=151.38
In triangle OAP tan 60 = AP ÷ OP
OP = tan 60× AP
=√3 × 15 =15√3
Area of triangle OAP = OP×AP ÷2
= 15 × 15 ÷2√3= 64.95
Area of shaded portion = Area of sector OAB - Area of triangle OAP
=151.38 - 64.95
= 86.43 cm²
Answer:
Step-by-step explanation:
Given :-
OA = 17 cm
AP = 15 cm
ΔOPA is right triangle.
Solution :-
Using Pythagoras theorem
OP = 8 cm
Area of shaded region = Area of sector AOBA - Area of ΔOPA
Area of shaded region = 60°/360° × πr² - 1/2 × b × h
Area of shaded region = 60°/360° × 22/7 × 17 ×17 - 1/2 × 8 × 15
Area of shaded region = 151.38 - 60
Area of shaded region = 91.38 cm²
Hence, the area of shaded portion is 91.38 cm².