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 the shaded region correct upto 2 decimal places. (Take $π = 3.142$ and $\sqrt{3} = 1.732$ )

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Solution

The area of the shaded section is going to be the area of the triangle minus the areas of the three sectors. Since it is an equilateral triangle, each sector is one sixth of the area of the circle with radius 4, which means the area of all three sectors is one half the area of the circle.

The area of a triangle is The base is 8 cm and the height $fraction numerator square root of 3 over denominator 2 end fraction a space sin c e space e q u i l a t e r a l space t r i a n g l e$

Area= $1 half cross times 8 cross times fraction numerator square root of 3 8 over denominator 2 end fraction equals 32 over 2 square root of 3 equals fraction numerator 55.424 over denominator 2 end fraction equals 27.712$

Area of 3 sectors=

now area of shaded portion =27.71-25.12=2.59 $c m^{2}$

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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 the shaded region correct upto 2 decimal places. (Take π=3.142 and √3=1.732)

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 the shaded region correct upto 2 decimal places. (Take $π = 3.142$ and $\sqrt{3} = 1.732$ )