Finding Area

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Site: TBAISD Moodle
Course: Michigan Geometry Preview 2012
Book: Finding Area
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Date: Sunday, May 19, 2019, 06:35 PM

Table of contents

Area of a Triangle

One formula for finding the area of a triangle, as stated in an earlier unit, is one-half of the base times the height or Area =  \frac{bh}{2} . In order to use this formula, we need to know the height of the triangle. There is another formula that can be used if we know two sides and the angle between them. In the triangle below, suppose we know sides a and b and angle C

Area Triangle

When a perpendicular line is drawn from the vertex A to side BC, we have the height, h. Because the resulting triangle is a right triangle, we can use the sine function and state:

area

Solving for h, the result is

h = b sin C

Substituting the new value for h into the original area formula, we obtain:

Area = 

 

ab sin C


2

 

This formula can be used for finding the area of any triangle. 
 
 
*Note:  Activity #1 in the overview of this unit is an activity that allows you to derive this formula through investigation.
 
 
Audio

Example

Find the area of the triangle below:

area ex

Step 1.  Identify the formula needed to find the area.

Since we were given 2 side lengths and an included angle, we will use the area formula that includes sine. 

aos ex 1

Step 2.  Substitute the values necessary to find the area.

aos ex 2

Step 3.  Use a calculator to solve the equation.

A = 83.2 square feet 

 

Audio

Video Lesson

For a video lesson on finding the area of a triangle, select the following link:

Determining the Area of a Triangle

Interactive Practice

For interactive practice using the Law of Sines to find the area of triangles, select the following link:

Finding Area Using Trigonometry

Practice

Finding Area Worksheet

Sources

Sources used in this book:

"Area of a Triangle and Parallelogram Using Trig." http://www.regentsprep.org/Regents/math/algtrig/ATT13/triareatrigprac.htm (accessed 06/20/11).

"Area of Triangle Using Trig." http://www.regentsprep.org/Regents/math/algtrig/ATT13/areatriglesson.htm (accessed 06/17/11).

Embracing Mathematics, Assessment & Technology in High Schools; A Michigan Mathematics & Science Partnership Grant Project

Holt, Rinehart & Winston, "Determining the Area of a Triangle." http://my.hrw.com/math06_07/nsmedia/lesson_videos/alg2/player.html?contentSrc=6505/6505.xml (accessed 5/16/2011).