The sides of a triangle are 8 cm, 15 cm, and 17 cm. At each of its vertices, circles of radius 3.5 cm are drawn. What is the area of the triangle excluding the portion covered by the sectors of the circles?
Show answer & explanation
Correct answer: D
Explanation
The correct answer is Option 4 i.e. 40.75cm2
As, 82 + 152 = 64 + 225 = 189 = 172
Hence, the triangle is a right-angled triangle.
Sum of the area of all the three sectors
= (180º/360º) × ᴨ × (3.5)2
= (1/2) × (22/7) × (7/2)2
= 19.25 cm2
And
Area of the triangle = (1/2) × AB × BC = (1/2) × 15 × 8 = 60 cm2
So, the remaining area = 60 - 19.25 = 40.75 cm2