A triangle of Sides 24 cm, 26 cm and 10cm. A Circle touching each of its vertices is drown, the radius of which is 4.2cm. Find the area of the covered area by the three segments of the circle?
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Answer:
100.75 cm²
19.25 cm² ( covered by circle inside triangle)
Step-by-step explanation:
The sides of the triangle are 10 cm, 24cm ,26cm. At each of its vertices, circle of radius 3.5 cm is drawn
Sides of triangle
10 , 24 & 26 cm
s = (10 + 24 + 26)/2 = 30
Area of Triangle using Hero formula = √30 (30-10)(30-24)(30-26)
= √30 * 20 * 6 * 4
= 120 cm²
Area Covered in triangle by 3 circles
= (θ₁ /360) πR² + (θ₂ /360) πR² + (θ₃ /360)πR²
θ₁ , θ₂ & θ₃ are three angles of triangle
=> θ₁ + θ₂ + θ₃ = 180°
= (( θ₁ + θ₂ + θ₃)/360) π (3.5)²
= (180 / 360) (22/7) (3.5)²
= (1/2) 11 * 3.5
= 19.25 cm²
Remaining area = 120 - 19.25 = 100.75 cm²
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