## Objective:

The student will be able to find the area of triangles using Heron's Formula and other trig techniques.

**Heron's Formula:** In a Δ let *a, b, c* be the sides, and let *A* be the area.

Heron's formula states --

The actual origin of this formula is somewhat obscure historically, and it may well have been known for centuries prior to Heron.

In the figure on the left, move points *A*, *B*, and *C* to solve the following:
- Find a triangle with perimeter 12 having integer area and integer sides.

- What different triangular regions could be formed by 10 meters of fencing?

What would be the area of each? What questions could you ask about the shapes or the areas?.

- Find a triangle having integer sides and integer area that is not a right triangle. Can you find others? Generalize.

**MECCA-Precalculus:** Online notes on using trig to find the area of a triangle (without the height). MECCA-Precalculus

A farmer has four straight pieces of fencing: 1, 2, 3, and 4 yards in length. What is the maximum area he can enclose by connecting the pieces? Assume the land is flat.