The sides of a triangle are 24 cm, 26 cm and 10 cm. At each of its vertices, circles of radius 4.2 cm are drawn. What is the area (in cm²) of the triangle, excluding the portion covered by the sectors of the circles? (π = 22/7)

Solution

26² = 24² + 10² The given triangle is a right angle triangle with the length of the base and height 24 cm and 10 cm and the length of the hypotenuse is 26 cm Area of the triangle = (1/2) × 24 × 10 = 120 cm² The radius of the circle in three vertices = 4.2 cm The total angle created in three circles in the vertices is 180° [∵ Sum of three angles of a triangle is 180°] The area of the triangle which is inside the common portion of the triangle and circle = (1/2) π (4.2)² = 27.72 cm The area of the triangle excluding the circle is (120 - 27.72) = 92.28 cm² ∴ The area excluding the portion covered by the section of the circles is 92.28 cm².