Question

# ABCD is a square of area 153.76 cm2. Find the area of the shaded part if P, Q, R, S are the midpoints of the sides.

Solution

## Area of the square =side × side=153.76 cm2 ⇒ side  = 12.4 cm [Formula] Area of the shaded region APQCRS = area of the square ABCD - area of the triangle PBQ - area of the triangle DSR Area of the triangle PBQ=12×(6.20×6.20)=19.22 cm2 [Since P and Q are the mid-points of the sides AB and BC] Area of the triangle DSR=12×(6.20×6.20)=19.22 cm2 [Since S and R are the mid-points of the sides AD and DC] So, Area of the shaded region =153.76−19.22−19.22=115.32 cm2 [Substitute and simplify]

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