Question

PQRS is a parallelogram,HSR is a straight line and HPQ=90°.if |HQ|=10cm and |PQ|=6cm,what is the area of the parallelogram

Answer 1

Given : PQRS is a parallelogram, HSR is a straight line and HPQ=90°. |HQ|=10cm and |PQ|=6cm,

To Find : The area of the parallelogram

Solution:

HSR is a straight line  and HPQ=90°.

=>PH ⊥ RS

Area of parallelogram = Base * height

=> Area of parallelogram = RS * PH

RS = PQ = 6   as opposite sides are equal

=> Area of parallelogram = 6 * PH

Now in right angle triangle HPQ

HQ² = PH²  + PQ²  ( using Pythagoras theorem )

=> 10²  = PH² + 6²

=> PH  = 8 cm

Area of parallelogram = 6 * PH

= 6 * 8

= 48  cm²

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