Question

1. A traffic signal board, indicating 'SCHOOL AHEAD'is an equilateral triangle with side. 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?​

Answer 1

This formula can be used for any triangle to calculate its area and it is very useful when it is not possible to find the height of the triangle easily . Heron's formula is generally used for calculating area of scalene triangle. Hence , the area of the signal board when perimeter is 180 cm is 900√3 cm²

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Answer 2

Answer:

perimeter of equilateral triangle = 3×side

180 cm = 3× side

side = 60cm

semi perimeter= perimeter/2 = 180/2 =90 cm

Area of equilateral triangle =

√90(90-60)(90-60)(90-60)

=√90×30×30×30

=100×3×3√3

=900√3 cm²