10. Heron's Formula

Theorem 10.1

The area of a triangle can be found using Heron's formula: \(A = \sqrt{s(s-a)(s-b)(s-c)}\), where \(s\) is the semi-perimeter \(\frac{a+b+c}{2}\).

Exercise 10.1

1. Calculate the area of a traffic signal board shaped as an equilateral triangle with perimeter 180 cm.
2. Determine the rent earned for a triangular advertisement wall with sides 122 m, 22 m, and 120 m at ₹5000 per square meter per year.
3. Find the painted area of a slide in a park with sides 15 m, 11 m, and 6 m.
4. Compute the area of a triangle with two sides 18 cm and 10 cm and perimeter 42 cm.
5. Solve for the area of a triangle with sides in the ratio 12:17:25 and perimeter 540 cm.
6. Find the area of an isosceles triangle with perimeter 30 cm and equal sides of 12 cm.

10.2 Summary