CBSE Class 10 Maths Areas of Combination of Figures

Please solve this question ?
 How to prove that opposite sides of a quadrilateral circumscribing a circle subtend supplementary angles at the centre of the circle

Find area of shaded region
 Two circular pieces of equal radii and maximum area, touching each other are cut out from a rectangular card board of dimensions 14 cm 7 cm. Find the area of the remaining card board. Use pie=22/7
 In the figure, a square OABC is inscribed in a quadrant OPBQ. If OA = 20 cm, find the area of the shaded region.
 The inside perimeter of a running track shown in the figure is 400 m. The length of each of the straight portions is 90 m, and the ends are semicircles. If the track is 14 m wide every where, find the area of the track. Also, find the length of the outer boundary of the track.
 Four equal circles are described about four corners of a square so that each touches two of the others, as shown in the figure. Find the area of the shaded region, if each side of the square measures 14 cm.
 In triangle ABC, angle A = 90^{o}, AB = 12 cm and BC = 20 cm. Three semicircles are drawn with AB, AC and BC as diameters. Find the area of the shaded portion.
 In the figure, ABC is an equilateral triangle of side 12 cm. The circle is centered at A with radius 6 cm. Find the area of the shaded region.
 Find the area of the region ABCDEFA shown in the figure, given that ABDE is a square of side 10 cm, BCD is a semi circle with BD as diameter, EF = 8 cm, AF = 6 cm and angle AFE = 90^{o}.