Question : 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? $\left(\pi=\frac{22}{7}\right)$
Option 1: 120
Option 2: 105.86
Option 3: 92.28
Option 4: 27.72
Correct Answer: 92.28
Solution : According to the question, Side of triangles = 24 cm, 26 cm, and 10 cm. Since $(26)^{2} = (24)^{2} + (10)^{2}$, then the triangle is right angles triangle. So, the area of triangle = $\frac{1}{2}$ × base × height = $\frac{1}{2}$ × 24 × 10 = 120 cm 2 Now, The area of the triangle is covered by 3 sectors with a total angle of 180° = $\frac{180}{360}\pi$ × (4.2) 2 = 27.72 cm 2 ⇒ area of the triangle excluding the area covered by the sectors = 120 – 27.72 = 92.28 cm 2 Hence, the correct answer is 92.28.
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Question : The sides of a triangle are 24 cm, 26 cm and 10 cm. At each of its vertex, circles of radius 4.2 cm are drawn. What is the area (in cm2) of the portion covered by the three sectors of the circle? $\left(\pi=\frac{22}{7}\right)$
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