- As more and more awareness is created to keep city clean, help in reducing
pollution, beautifying the city. You must have noticed in Metro and other places
of the city, the walls are decorated with art pieces and paintings. One such
painting on a wall is in the form of an equilateral triangle of area 493 m. It is
noticed that taking each angular point as centre circles have been described with
radius equal to half the length of the side of the triangle. There is some area of
the triangular part not included in the circles.
(i) What is the perimeter of an equilateral triangle?
(ii) Find the area of the triangle not included in the circles.
Answers
Question - As more and more awareness is created to keep city clean, help in reducing pollution, beautifying the city. You must have noticed in Metro and other places of the city, the walls are decorated with art pieces and paintings. One such
painting on a wall is in the form of an equilateral triangle of area 49√3 sq m. It is noticed that taking each angular point as center circles have been described with radius equal to half the length of the side of the triangle. There is some area of triangular part not included in the circles.
(i) What is the perimeter of an equilateral triangle?
(ii) Find the area of the triangle not included in the circles.
Answer - (i) 42 m
(ii) 7.77 sq m
(i) area of triangle = 49√3 sq m
⇒ √3/4 side^2 = 49√3
⇒ side^2 = 49 * 4 = 7^7 * 2^2
⇒ side = 14 m
perimeter = 3 * side = 3 * 14 m = 42 m
(ii) area not included = area of triangle - area of 3 circles
= 49√3 - [ 3 * (60°/360°) * 22/7 * 7 * 7 ]
= 84.77 - 77 sq m
= 7.77 sq m