Question

in figure ABC is an equilateral triangle of side 8 cm A B and C are the centres of circular arcs of radius 4 cm find the area of shaded region

Answer 1

Area of a sector (circular arc)
$(angle \: of \: sector \: in \: degrees \div 360) \times \pi \times {r}^{2}$

Area of an equilateral triangle is
$( \sqrt{3} \div 4) {a}^{2}$
Here radius of sector is 4cm, and angle is 60 degrees.
a is side of equilateral triangle which is given as 8cm
Hence area of shaded portion = Area of equilateral triangle - (3 * Area of one sector)

Answer 2

Answer:

The area of shaded region is 2.576 cm² .

Step-by-step explanation:

Given :

Side of equilateral ∆ PQR , a = 8 cm

Radius of each circular arcs, r = 4 cm

Sector angle , θ = 60°

[Each Angle in equilateral triangle is 60°]

Area of shaded region, A = Area of equilateral ∆PQR -  3 × Area of sector

A = √3/4 × side² - 3 [θ/360° × πr²]  

A = √3/4 × 8² - 3 [60°/360° × π× 4²]

A = √3/4 × 64 - 3 [1/6 × π× 16]

A = √3/4 × 64 - 3 [1/6 × π× 16]

A = √3 × 16 - 3[8π/3]

A = √3 × 16 - 8π

A = 1.732 × 16 - 8 × 3.142

[Given √3 = 1.732 & π =  3.142]

A = 27.712 - 25.136

A = 2.576 cm²

Area of shaded region = 2.576 cm²

Hence, the area of shaded region is 2.576 cm² .