Question

Find the area of the shaded region in the adjoining figure, given that PS=11cm, QR=19cm, RS=17cm and<SPQ=<PQR=90°.​

Answer 1

ASR is a right angle triangle,

AR = 8cm { 19-11}

By Pythagoras theorem,

AR² + AS² = SR²

8² + AS² = 17²

64 + AS² = 289

AS = √289 - 64

AS = 15cm

Area of the triangle ASR = 1/2×b×h

=1/2x15x8

=15x4

=60cm²

PQRS is a rectangle,

PS = 11cm

AS = 15cm

Area of the rectangle = lxb

= 11x 15

= 165cm²

The total area of the shades region = 60cm² + 165cm²

= 225cm²

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