Question

The area of an equilateral triangle is 100√3 cm square taking each vertex as centre a circle is described with radius equal to half the length of the side of the triangle find the area of that part of the triangle which is not included in the circles.take π=3.14 and √3=1.732

Answer 1

I hope this answer would be helpful for you

Answer 2

the area of that part of the triangle which is not included in the circles is 16.2

•Step 1

ABC is an equilateral triangle.

as all angles equal 60°

Area of ΔABC = 100√3

•Step 2

Let side = a

as we know √3/4. (side)² = 100√3

(a)² = 100√3× 4/√3

(a)² = 400

a = 20 I'm

.Step 3

The radius of the circles = 20/2 cm

= 10 I'm

Step 4.

Area of 1 sector = (60°/360°) × π r²

= 1/6 × 3.14 × (10)²

= 314/6

.Step 5

Area of 3 sectors = 3 × 314/6= 157

Area of the shaded region = Area of equilateral ΔABC - Area of 3 sectors

= 100√3- 157

= 173.2 - 157

= 16.2