# How do you use Heron's formula to determine the area of a triangle with sides of that are 25, 28, and 22 units in length?

##### 2 Answers

Area of triangle is

#### Explanation:

Heron's formula gives the area of a triangle with sides

Hence to determine the area of a triangle with sides of

Hence area of triangle is

#### Explanation:

Heron's formula is usually among the poorest choices. Here are some modern forms:

For a triangle with sides

The last is of course Heron.

Usually given integer sides the factored form is fast and leads to the least messy exact answer:

If we're given 2d coordinates, the Shoelace Theorem is the quickest way to the area. If we're given 3 or more dimensional coordinates, the first two forms, which rely only on squared lengths, are best.

The first form is great for deriving the special cases as well:

**Equilateral triangle** :

**Isosceles triangle**:

**Right Triangle**

Cool. I'm not sure why they don't teach it in school.