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? $(\pi=\frac{22}{7})$

92.28

We have a concept,

The area made by three circles in three vertices of a triangle of the same radius will be half the area of the circle.

We have given,

The sides of the triangle = 24 cm, 26 cm, and 10 cm.

The radius of the circle in three vertices = 4.2 cm

As the triangle is a right angled triangle,

Area of the triangle = \(\frac{1}{2}\) × 24 × 10 = 120 cm²

The total angle created in three circles in the vertices = 180° 

The area of the triangle which is inside the common portion of the triangle and circle = \(\frac{1}{2}\) × \(\frac{22}{7}\) ×  (4.2)² = 27.72 cm²

The required area =  (120 - 27.72) = 92.28 cm²