Multiple choice

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 section of the circles?

  1. 120

  2. 27.72

  3. 92.28

  4. 105.86
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Sides 24, 26, 10 form a right triangle (10² + 24² = 26²). Area = 1/2 × 10 × 24 = 120 cm². Three circles of radius 4.2 cm at vertices with angles 90°, ~67.38°, ~22.62° cover total sector area = (90+67.38+22.62)/360 × π × 4.2² = 180/360 × (22/7) × 17.64 = 27.72 cm². Triangle excluding circles = 120 - 27.72 = 92.28 cm².

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