The area of an equilateral triangle is 9√3 cm2
. Taking each angular point as centre, circle is drawn
with radius equal to half the length of the side of the triangle. Find the area of triangle not included
in the circles. [Take √3=1.73]
Answers
Given : The area of an equilateral triangle is 9√3 cm²
Taking each angular point as centre, circle is drawn with radius equal to half the length of the side of the triangle.
To Find : the area of triangle not included in the circles.
Solution:
area of triangle not included in the circles. = area of triangle - area of circles inside triangle
area of an equilateral triangle = (√3 / 4) side²
(√3 / 4) side² = 9√3
=> side² = 36
=> Side = 6 cm
Radius = 3 cm
Each angle of sector for circle inside triangle is 60°
Area of Each sector = ( sector angle / 360° ) π(radius)²
=> Area of Each sector = ( 60° / 360°) π (3)²
=> Area of Each sector = 3π/2 cm²
Area of 3 sectors = 3 * 3π/2 = 9π/2 cm²
area of triangle not included in the circles. = 9√3 - 9π/2
√3 = 1.73
π = 3.14
= 9 (1.73) - 9(3.14/2)
= 9 ( 1.73 - 1.57)
= 9 ( 0.16)
= 1.44 cm²
the area of triangle not included in the circles is about 1.44 cm²
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Answer:
area of an equilateral triangle =(√3/4) side²
(√3/4) side² = 9-√3
=> side² = 36
=> Side = 6 cm
Radius 3 cm
Each angle of sector for circle inside triangle is 60°
Area of Each sector = (sector angle / 360°) П(radius)²
=> Area of Each sector = (60° / 360°) TT (3)² => Area of Each sector = 3π/2 cm²
Area of 3 sectors = 3* 3π/2 = 9π/2 cm²
area of triangle not included in the circles. = 9-√3 - 9π/2
√3 = 1.73
pi = 3.14
= 9 (1.73) - 9(3.14/2)
9 (1.73 -1.57)
= 9 (0.16)
= 1.44 cm²