Find the area of a triangle with side lengths 7 m, 8 m, and 9 m.

Question: Find the area of a triangle with side lengths 7 m, 8 m, and 9 m.

Solution:

We know, the semi-perimeter of the triangle:
S = (a + b + c)/2
S = (7 + 8 + 9)/2
S = 24/2
∴ S = 12

Area of the triangle = √[S(S - a)(S - b)(S - c)]
= √[12 × (12 - 7) × (12 - 8) × (12 - 9)]
= √[12 × 5 × 4 × 3]
= √720
= 12√5

∴ The area of the triangle = 12√5 m².