The sides of a triangle are 24 cm, 26 cm, and 10 cm, At least of its vertices, a circle of radius 4.2 cm is drawn, What is the area ( in cm2) of the triangle, excluding the portion covered by the sectors of the circles?
( π = )
Show answer & explanation
Correct answer: D
Explanation
The correct answer is option 4 i.e. 92.28
The sides of the triangle are 24 cm, 26 cm, and 10 cm.
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
676 = 576 + 100
676 = 676
The given triangle is a right-angle triangle with the length of the base and height of 24 cm and 10 cm and the length of the hypotenuse is 26 cm.
Area of the triangle = (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 1800
The area of the triangle which is inside the common portion of the triangle and circle = (π/2)(4.2)2 = 27.72 cm2
The area of the triangle excluding the circle = (120 - 27.72) = 92.28 cm2