the area of an equilateral triangle is 49√ 3cm.taking each angular point as centre,circle is drawn with radius equal to half the length of the side of triangle.find the area of triangle not included in the circles.take √ 3 =1.73
Answers
FIGURE IS IN THE ATTACHMENT
GIVEN:
Area of ∆ABC = 49√3
θ = 60° (angle of an equilateral ∆)
Let the each side of the ∆ be a cm.
Area of equilateral triangle = (√3/4) × side ²
49√3 = (√3/4) × a²
a² = 49√3 ×( 4 /√3) = 49 × 4
a= √49 × 4 = 7 × 2 = 14 cm
Radius of the circle half the length of the side of the ∆ABC (GIVEN)
Radius of the circle = ½ × 14 = 7 cm
Area of sector =(θ/360) × πr²
Area of sector = (60/360) × 22/7 × 7²
= ⅙ × 22 × 7= 154/6 = 77/3 cm²
Required area = Area of ∆ABC - 3 ( area of a sector of angle 60° in a circle of radius 7 cm)
Required area = 49√3 - 3×77/3
= 49√3 - 77
= 49 × 1.73 -77 = 84.77 - 77 = 7.77 cm²
Hence, the area of the triangle not included in the circle is 7.77 cm²
HOPE THIS WILL HELP YOU...
Area of the equilateral triangle = √3/4a²=49√3
side of the triangle a=√(49*4)=7*2=14cm
radius of the circle =14/2 = 7cm
angle of an equilateral triangle = 60°
Area of the sector of the circle inside the triangle = theta/360°*π*r²=60°/360°*π*7²=π/6*7*7
Area of the triangle not included = Area of traingle - 3*area of the sectors on each vertex = 49√3-3*π*7*7/6 = 7.84cm²