Lesson Materials

## 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:
1. Find a triangle with perimeter 12 having integer area and integer sides.

2. 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?.

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

No hands-on yet

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.