Question

find the area of the triangle whose sides are 18 cm 24cm and 30cm

Answer 1

We identify that the sides are are:
18 : 24 : 30 = 3 : 4 : 5.

As 3^2 + 4^2 = 5^2, it is a Right angle triangle.

Area = 1/2 × 18 × 24 = 216 cm^2.

In general we can use the formula:
s = (a+b+c)/2 = 36.
Area = Sqrt[ s (s - a) (s - b) (s - c) ]
= Sqrt[ 36 × 18 × 12 × 6]
= Sqrt(36× 3×6×3×4×6)
= 6×3×6×2= 216 cm^2.

Answer 2

A method for calculating the area of a triangle when you know the lengths of all three sides.

Let a,b,c be the lengths of the sides of a triangle. The area is given by:
Area = √ p ( p − a ) ( p − b ) ( p − c )
where p is half the perimeter, or
a + b + c
2
Therefore, p=24+18+30/2=36.
Now, area =√36*12*6*18=216.