|Course:||Michigan Geometry Preview 2012|
|Printed by:||Guest user|
|Date:||Wednesday, July 17, 2019, 10:42 AM|
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 = . 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
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:
Solving for h, the result is
h = b sin C
Substituting the new value for h into the original area formula, we obtain:
ab sin C
Find the area of the triangle below:
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.
Step 2. Substitute the values necessary to find the area.
Step 3. Use a calculator to solve the equation.
A = 83.2 square feet
For a video lesson on finding the area of a triangle, select the following link:
For interactive practice using the Law of Sines to find the area of triangles, select the following link:
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).