Question

Protul has drawn an equilateral triangle ABC picture beside of which length of each side is 10 cm. Sumita has drawn three circular arcs centering A, B, C with the length of radius 5 cm. and has coloured some portion at the middle. let us write by calculating the area of coloured portion at the middle
please answer ASAP​

Answer 1

Step-by-step explanation:

Given: ∆ABC is an equilateral triangle with side 10 cm, Arcs centered at B and C have radius 5 cm.

We need to find the area of the colored portion.

Area of colored portion = Area of ∆ABC – Area of sectors centered at B and C.

∵ ∆ABC is an equilateral triangle

We know that

Area of a equilateral triangle where a is the side of it.

⇒ Area of ∆ABC = 43.3cm2

For the sectors,

Radius = 5 cm and angle subtended = 60°

{∵∆ABC is an equilateral triangle and each angle of it is 60°}

We know that the area of the minor sector

⇒ Area of sector centered at

⇒ Area of sector centered at B =13.095 cm2

Total area of both the sectors centered at B and C = 13.095 + 13.095 = 26.19 cm2

⇒ Area of colored portion = 43.3 – 26.19 = 17.11 cm2