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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.

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 $Y2=\frac{1}{2} \cdot 3 \cdot 4$ 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.

Feb 23, 2012

Nov 04, 2014