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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


Team Careers360 25th Jan, 2024
Answer (1)
Team Careers360 26th Jan, 2024

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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