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6.1: Analyzing Heron’s Formula

Difficulty Level: At Grade Created by: CK-12

This activity is intended to supplement Trigonometry, Chapter 5, Lesson 2.

Problem 1 - Consider a 3, 4, 5 right triangle.

  • Draw the triangle.
  • Find the area using A=\frac{1}{2}bh.
  • Consider Heron’s Formula, A=\sqrt{s(s-a)(s-b)(s-c)}

In Y=, plug into Y1= \sqrt{x(x-3)(x-4)(x-5)}. Zoom in by changing the window. Press WINDOW and change the parameters to the right.

Press GRAPH.


Xmin = -1

Xmax = 8

Xscl = 1

Ymin = -1

Ymax = 10

Yscl = 1

Xres = 1

  • Describe the graph. Does it have any x or y intercepts?
  • In Y2, type Y2=\frac{1}{2} \cdot 3 \cdot 4 or 6, the area of this triangle. Press GRAPH. Do the two functions intersect? If so, write the point(s) below.
  • Y1 is Heron’s formula with a = 3, b = 4, and c = 5 and s = x. What do the point(s) above tell us about this specific Heron’s formula? What do (x, \ y) represent?

Problem 2

Repeat the steps from Problem 1 with the triangle below.

Are your findings the same?

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Date Created:

Feb 23, 2012

Last Modified:

Nov 04, 2014
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