In the adjacent figure A,B,C and D are centers of equal circles which touch externally is pairs and ABCD is a square of side 7cm. Find the area of the shaded region.
Answers
given,
A,B,C,D are the centres of the circles which touch externally
side of a square ABCD=7cm
Radius of a circle =7÷2 cm
Area of a square = 7×7 = 49cm²
These are four equal sector with angle at the centre =90°
Area of shaded region = Area of square - Area if 4 equal sectors
49-(4 × x°/360 × πr²)
49-(4 × 90°/360 × 22/7 × 7/2 × 7/2)
49- 77/2
49- 38.5
10.5 cm²
hope it helps!!
ABCD IS A SQUARE . SO AREA OF SQUARE = 7×7= 49
AREA OF QUADRANT OF CIRCLE =
22×7×7 / 7 ×4 ×2 ×2 = 77 / 8
AREA OF 4 QUADRANTS = 4× 77/8 = 77/ 2
AREA OF SHADED REGION = AREA OF 4 QUADRANTS - AREA OF SQUARE = 77/2- 49 = 77- 98/2 = 21/2 = 10.5 ANS
( we used area of quadrant because it's a quadrant i.e. one fourth part of a circle . We can't use the formula of area of sector .