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.
Related Questions
Know More about
Staff Selection Commission Sub Inspector ...
Result | Eligibility | Application | Selection Process | Cutoff | Admit Card | Preparation Tips
Get Updates Brochure
Your Staff Selection Commission Sub Inspector Exam brochure has been successfully mailed to your registered email id “”.
