Q. 1275.0( 3 Votes )

# ABCD is a given rectangle with length as 80 cm and breadth as 60 cm. P, Q, R, S are the mid points of sides AB, BC, CD, DA respectively. A circular rangoli of radius 10 cm is drawn at the centre as shown in Fig. 9.69. Find the area of shaded portion.

Answer :

Given, P is the mid point of AB, so AP = 40 cm

And S is the mid point of AD, so AS = 30 cm

Area of ABCD = 80 × 60 = 4,800 cm^{2}

Area of ∆SAP = × AP × AS = × 40 × 30 = 600 cm^{2}

Area of 4 unshaded congruent triangles =4 × 600 cm^{2} = 2,400 cm^{2}

Area of unshaded circle = ∏r^{2} = 3.14 × 10 × 10 = 314 cm^{2}

∴ Area of shaded area = 4,800 – (2,400 + 314) = 2086 cm^{2}

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