Question

In the figure below, AB is a diameter of the circle and PQ is a chord parallel to it.

Compute the area of the quadrilateral ABQP.

Answer 1

Given: Two parallel chords PQ and AB of lengths 8 cm and 16 cm

Also, AB is the diameter of the given circle.

Construction: Draw OD ⊥ PQ

Radius of the circle = = 8 cm

We know that PQ = 2PD = 2, where r is the radius of the circle and d is the perpendicular distance of PQ from the centre of the circle.

⇒ 8 = 2

⇒ = 4

⇒ 8² − d² = 4²

⇒ d² = 64 − 16 = 48

⇒ d =

⇒ OD = cm

We know that area of a trapezium = × Sum of parallel sides × Distance between them

∴ Area of trapezium, ABQP = × (8 + 16) cm × cm

= cm²