Theory question 104
Mensuration of Plane Shapes(a) In the diagram, O is the centre of the circle radius r cm and ∠XOY = 90°. If the area of the shaded part is 504 cm2, calculate the value of r. [Take π = 22/7]
(b) Two isosceles triangles PQR and PQS are drawn on opposite sides of a common base PQ. If ∠PQR = 66° and ∠PSQ = 109°, calculate the value of ∠RQS.
Show the model answer
Model answer
(a) Segment = sector − triangle: (90/360)(22/7)r2 − ½r2 = (11/14 − 7/14)r2 = (2/7)r2 = 504.
r2 = 1764, so r = 42 cm.
(b) In isosceles ΔPQS (PS = QS): ∠SQP = (180° − 109°)/2 = 35.5°.
∠RQS = ∠PQR + ∠PQS = 66° + 35.5° = 101.5°.
Explanation
The shaded part is a minor segment: sector minus the right-angled triangle.