Question

In the given figure, ABCD is a rectangle in which AB = 60 cm and BC = 40 cm. If P, Q, R and S be the mid-points of AD, DC, CB and BA, find the area of the shaded region.
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Answer 1

Answer:

40√13

Step-by-step explanation:

Construction: Draw AC

AC² = AB² + AC²

AC² = 60² + 40²

AC² = 3600 + 1600

AC = √5200

In Triangle ADC, P and Q are the mid points of AD and DC respectively.

∴ BY mid point theorem, PQ = 1/2 of AC

Similarily SR = QR = PS = 1/2 × √5200

∴ PQRS is  a ║gm.

∴ AREA of PQRS = 4×1/2×√5200

                            = 2 × 20√13

                            = 40√13 cm

Answer 2

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