In a rhombus PQRS, side PQ = 17 cm and diagonal PR = 16 cm. Calculate the area of the rhombus.
Pythagoras Theorem
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Question

In a rhombus PQRS, side PQ = 17 cm and diagonal PR = 16 cm. Calculate the area of the rhombus.

KnowledgeBoat · Accepted Answer

We know that, The diagonals of a rhombus bisect each other at right angles. From figure, OP = OR = 8 cm PQ = 17 cm In right angled △ POQ, Hypotenuse2 = Perpendicular2 + Base2 ⇒ PQ2 = OP2 + OQ2 ⇒ 172 = 82 + OQ2 ⇒ 289 = 64 + OQ2 ⇒ OQ2 = 289 - 64 ⇒ OQ2 = 225 ⇒ OQ = ⇒ OQ = 15 cm. Since, OQ = OS = 15 cm (the diagonals of a rhombus bisect each other) QS = OQ + OS = 15 + 15 = 30 cm ∴ Diagonals are PR = 16 cm and QS = 30 cm. As we know, Area of rhombus = × Product of diagonals = = 240 cm2. Hence, the area of rhombus = 240 cm2.

Mathematics

In a rhombus PQRS, side PQ = 17 cm and diagonal PR = 16 cm. Calculate the area of the rhombus.

Pythagoras Theorem

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