Explanation
Step 1 : Find the sides of triagnle
Let the sides of the triangle be 12a, 25a, 17a We know that perimeter of the triangle = Sum of all sides
⇒ 12a + 25a + 17a = 54a
Given, perimeter of the triangle = 540 m ⇒54a = 540 m a = 10 m So, the lengths of the sides of triangle are
12a = 120 m
25a = 250 m
17a = 170 m
Step 2 : Find the area of triangle using Heron's formula
We can use Heron's formula to get the area of triangle
Area of triangle with sides with sides a, b, c and semi perimeter s
are √s(s−a)(s−b)(s−c) respectively.
and s = a+b+c2
For triangle with sides 120 m, 250 m and 170 m,
s = 120+250+1702
s = 270 m Substituting the sides 120 m, 250 m and 170 m in the Heron's formula, we get
⇒A=√270(270−120)(270−250)(270−170)
=√270×150×20×100
=√9×30×30×5×20×20×5
=3×30×5×20
=9000m2
Hence , area of triangle is 9000 m2
A traffic signal board, indicating 'SCHOOLAHEAD', is an equilateral triangle with side a. Find the area of the signal board, using Heron's formula. If its perimeter is 180cm, what will be the area of the signal board?
Please disable the adBlock and continue. Thank you.