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The sides of square PQRS are extended by sides of equal length to form square ABCD if RD = 6 cm and area of PQRS is 100 sq. cm. then, what is the area (in sq. cm) of ABCD?

The sides of square PQRS are extended by sides of equal length to form square ABCD if RD = 6 cm and area of PQRS is 100 sq. cm. then, what is the area (in sq. cm) of ABCD? Correct Answer 292

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Area of the square PQRS = 100 sq.cm.

(side)2 = 100

⇒ side = 10cm

RD = 6 cm

By Symmetry, RD = AS = BP = QC = 6 cm

In ΔARD –

AR = (6 + 10) = 16 cm

RD = 6 cm

Area of ΔARD = 1/2 × RD × AR = 1/2 × 6 × 16 = 48 sq.cm.

Thus, Area of square ABCD = (4 × 48) + 100 = 192 + 100 = 292 sq.cm.

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