Advertisements
Advertisements
Question
A traffic signal board, indicating ‘SCHOOL AHEAD’, is an equilateral triangle with side ‘a’. Find the area of the signal board, using Heron’s formula. If its perimeter is 180 cm, what will be the area of the signal board?
Advertisements
Solution
The side of the traffic signal board = a
Perimeter of traffic signal board = 3 × a
2s = 3a ⇒ s = `3/2 a`
By heron's formula,
Area of triangle = `sqrt(s(s-a)(s-b)(s-c))`
Area of given triangle = `sqrt(3/2 a(3/2a-a)(3/2a-a)(3/2a-a))`
= `sqrt((3/2a)(a/2)(a/2)(a/2))`
= `sqrt3/4a^2` ... (1)
Perimeter of traffic signal board = 180 cm
Side of traffic signal board (a) = `(180/3) cm` = 60 cm
Using equation (1), the area of the traffic signal board
= `sqrt3/4(60cm)^2`
= `(3600/4sqrt3)cm^2` = `900sqrt3 cm^2`
APPEARS IN
RELATED QUESTIONS
The perimeter of an isosceles triangle is 42 cm and its baše is (32) times each of the equal sides. Find the length of each side of the triangle, area of the triangle and the height of the triangle.
Find the area of the shaded region in the given figure.
Find the area of a triangle whose base and altitude are 5 cm and 4 cm respectively.
Find the area of an isosceles triangle having the base x cm and one side y cm.
The perimeter of an equilateral triangle is 30 cm. The area is
The triangular side walls of a flyover have been used for advertisements. The sides of the walls are 13 m, 14 m and 15 m. The advertisements yield an earning of Rs 2000 per m2 a year. A company hired one of its walls for 6 months. How much rent did it pay?
The sides of a quadrilateral ABCD are 6 cm, 8 cm, 12 cm and 14 cm (taken in order) respectively, and the angle between the first two sides is a right angle. Find its area.
How much paper of each shade is needed to make a kite given in the following figure, in which ABCD is a square with diagonal 44 cm.
The perimeter of a triangle is 50 cm. One side of a triangle is 4 cm longer than the smaller side and the third side is 6 cm less than twice the smaller side. Find the area of the triangle.
In the following figure, ∆ABC has sides AB = 7.5 cm, AC = 6.5 cm and BC = 7 cm. On base BC a parallelogram DBCE of same area as that of ∆ABC is constructed. Find the height DF of the parallelogram.
