How do you use Heron's formula to find the area of a triangle with sides of lengths #29 #, #25 #, and #22 #?

This is a 2 step process

step 1 : Find half the perimeter ( s ) of the triangle

let a = 29 , b = 25 and c = 22

step 2 : Calculate the area (A ) using

To use Heron's formula to find the area of a triangle with sides of lengths 29, 25, and 22, first calculate the semi-perimeter of the triangle. Then, apply Heron's formula, which states that the area of a triangle with sides of lengths a, b, and c and semi-perimeter s is given by the square root of s times (s - a) times (s - b) times (s - c).

The semi-perimeter (s) is calculated as the sum of the lengths of the sides divided by 2:

s = (29 + 25 + 22) / 2 = 76 / 2 = 38

Now, apply Heron's formula:

Area = √(s * (s - a) * (s - b) * (s - c))

Area = √(38 * (38 - 29) * (38 - 25) * (38 - 22))

Area = √(38 * 9 * 13 * 16)

Area = √(358176)

Area ≈ 598.884

Therefore, the area of the triangle with sides of lengths 29, 25, and 22 is approximately 598.884 square units.