# Use Heron's Area Formula to find the area of the triangle. a = 33, b = 36, c = 25

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### 2 Answers

Heron's formula allows finding the area of any triangle, knowing the lengths of its sides.

According to the formula of Heron, the area of a triangle with sides **a**, **b** and **c**, has the following expression:

A = √[s(s-**a**)(s-**b**)(s-**c**)]

In the formula, the amount **s** is the semiperimeter of the triangle, which is half the sum of the lengths of all sides:

**s** = (**a** + **b** + **c**)/2

For the given triangle, the sides are:

a = 33, b = 36 and c = 25

Applying the above formulas, we have:

s = (33 + 36 + 25)/2 = 47 units of length.

A = √[47(47-33)(47-36)(47-25)] = √(159.236)

A= 399 units of area.

**So the area of this triangle is 399 units of area.**

**As no units are specified, we used the "units of area" to express the units of the result.**

Heron's formula gives the area of a triangle with sides a, b and c as `A = sqrt(s*(s - a)*(s - b)(s-c))` where is the semi-perimeter `s = (a +b + c)/2`

For a triangle with sides a = 33, b = 36, c = 25, s = `(33 + 36 + 25)/2 = 47` .

The area of the triangle is:

A = `sqrt(47*(47 - 33)*(47 - 36)*(47 - 25))`

= `sqrt(47*14*11*22)`

= `22*sqrt(329)`

The area of a triangle with sides a = 33, b = 36, c = 25 is `22*sqrt(329)`