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6.1: Analyzing Heron’s Formula

Difficulty Level: At Grade Created by: CK-12
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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=12bh.
  • Consider Heron’s Formula, A=s(sa)(sb)(sc)

In Y=, plug into Y1=x(x3)(x4)(x5). Zoom in by changing the window. Press WINDOW and change the parameters to the right.

Press GRAPH.

WINDOW

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=1234 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?

Notes/Highlights Having trouble? Report an issue.

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Date Created:
Feb 23, 2012
Last Modified:
Nov 04, 2014
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