With centres A, B, C and D, four circles are drawn such that each circle touch externally two of the remaining three circles. In the given figure, ABCD is a square of side 14 cm. Find the area of the design (shaded region). In a circular table cover of radius 32 cm, a design is formed leaving an equilateral triangle ABC in the middle as shown in the figure. So, area of remaining portion of square `= 16 – 6.28 = 22.28 sq cm` Solution: Area of square `= text(Side)^2 = 4^2 = 16 sq cm`Īrea of cut portion = Area of two circles = 1 circle + 4 quadrants Find the area of the remaining portion of the square. From each corner of a square of side 4 cm a quadrant of a circle of radius 1 cm is cut and also a circle of diameter 2 cm is cut as shown in the figure. Solution: Area of sector outside triangleĪrea of shaded region `= 94.28 + 62.352 = 156.632 sq cm` Find the area of the shaded region in the given figure, where a circular arc of radius 6 cm has been drawn with vertex O of an equilateral triangle OAB of side 12 cm as centre. Solution: Area of Square `= text(Side)^2 = 14^2 = 196 sq cm`Īrea of shaded region `= 196 – 154 = 42 sq cm` Find the area of the shaded region in the given figure, if ABCD is a square of side 14 cm and APD and BPC are semicircles.

If R and r are the two radii, then area of shaded region = Area of Bigger Sector – Area of Smaller Sector Find the area of the shaded region in the given figure, if radii of the two concentric circles with centre O are 7 cm and 14 cm respectively and angle AOC = 40°. Solution: Here, OR is the hypotenuse of ∆PQR, because lines from two ends of diameter always make a right angle when they meet at circumference.Īrea of triangle `= ½ xx text(base) xx text(height)` Find the area of the shaded region in the given figure, if PQ = 24 cm, PR = 7 cm and O is the centre of the circle.

Ex 12.3 class 10