Question

The sides of a triangle are 10cm, 24cm and 26cm. At each of its vertices

Answer 1

Answer:

Step-by-step explanation:

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