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

Expert Answers
electreto05 eNotes educator| Certified Educator

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.

tonys538 | Student

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)`