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 * **Aim: How do we find the area of any triangle knowing two adjacent sides and the included angle?** //(This formula is on your Regents Reference Sheet)//

At the end of this lesson, you will be able to... 1. investigate and discover the formula for the area of a triangle in terms of two sides and the sine of the included angle 2. conjecture and apply the formula A=½absinC for the area of a parallelogram in terms of two sides and the included angle 3. apply either formula to to solve problems, including real-world applications involving triangles and parallelograms

In this lesson you will watch two videos. The first video will explain how we can change the triangle area formula you know, A=½bh, to A=½absinC. Video 2 will talk about how this formula is related to the parallelogram area formula. There will also be problems presented.

Copies these questions down in your notebooks. Answer them as you watch the videos.


 * 1) What is the new area formula for any triangle?
 * 2) How is area formula for a triangle related to the area formula for a parallelogram?
 * 3) What are the things you need to know in order to use these formulas?
 * 4) What is a rhombus?

[|Video 1]

[|Video 2]


 * Classwork:** Try some of your own. Make sure to draw a picture first. Remember you need to know two sides and the angle between them.

1. Find the area of triangle DEF if DE+ 14, EF = 9, and the measure of angle E = 30. (Answer: 31½) 2. The adjacent sides of parallelogram ABCD measure 15 and 12. The measure of the angle between them is 135°. Find the area of the parallelogram in simplest radical form. (Answer: 90sqrt2 units²)


 * **Homework:**




 * **Answers:**




 * **Journal entry:** The area of a triangle can be determined using either of the following formulas: A = ½bh or A = ½absinC. Explain how those two formulas are related.