Theory question 104
Mensuration of Plane ShapesThe area of a circle is 154 cm2. It is divided into three sectors such that two of the sectors are equal in size and the third sector is three times the size of the other two put together. Calculate the perimeter of the third sector. [Take π = 22/7]
Show the model answer
Model answer
22/7 × r2 = 154 → r2 = 49 → r = 7 cm.
Angles a, a and 3(2a) = 6a: 8a = 360° → a = 45°, so the third sector is 270°.
Arc = 270/360 × 2 × 22/7 × 7 = 33 cm.
Perimeter = 33 + 7 + 7 = 47 cm.
Explanation
The perimeter of a sector is its arc plus two radii.