CBSE Class 10 Maths Question Paper 2018 | Q20

Question 20: Find the area of the shaded region in figure given below, where areas drawn with centres A, B, C, and D intersect in pairs at mid – points P, Q, R and S of the sides AB, BC, CD and DA respectively of a square ABCD of side 12 cm.

Video Explanation

Explanatory Answer | CBSE Class 10 Board Paper 2018 Q20

ABCD is a square of side 12 cm
P, Q, R and S are mid points of AB, BC, CD and DA respectively

∴ AP = PB = BQ = QC = CR = RD = DS = SA = 6 cm
Radii of all arcs with A, B, C and D as centers are 6 cm each.

Area of shaded region = Area of square of side 12 cm - Sum of areas of 4 equal sectors.

Area of square = 12 × 12 = 144 sq cm
Each sector subtends an angle of 90^o.
∴ Area of each sector = \\frac{90}{360}) × π × 6² = \\frac{1}{4}) × 3.14 × 36
Sum of areas of all 4 sectors = 4 × \\frac{1}{4}) × 3.14 × 36 = 3.14 × 36 = 113.04 sq cm.

∴ Area of shaded region = 144 - 113.04 = 30.96 sq cm.