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 cm) of the portion covered by the three sectors of the circle?
Show answer & explanation
Correct answer: D
Explanation
The correct answer is Option 4 i.e 27.72.
Given:
The sides of the triangle are 24 cm, 26 cm, and 10 cm.
Concept Used:
The area made by three circles in three vertices of a triangle of the same radius will be half the area of the circle.
262 = 242 + 102
The given triangle is a right-angle triangle with a length of the base and height of 24 cm and 10 cm and the length of the hypotenuse is 26 cm
The area of the triangle is (1/2) × 24 × 10 = 120 cm2
The radius of the circle in three vertices is 4.2 cm
The total angle created in three circles in the vertices is 180° [" Sum of three angles of a triangle is 180°]
The area of the triangle which is inside the common portion of the triangle and circle is (1/2) π (4.2)2 = 27.72 cm2
Thus,
The area (in cm) of the portion covered by the three sectors of the circle is 27.72 cm2