11.2 Areas of Parallelograms and Triangles Objective: After studying this section you will be able to find the areas of parallelograms and triangles

The Area of a Parallelogram We can “cut and paste” to find the area of a parallelogram. base (b) height (h) cut paste =

Theorem. The area of a parallelogram is equal to the Theorem The area of a parallelogram is equal to the product of the base and the height for that base. where b is the length of the base and h is the height

The Area of a Triangle The area of any triangle can be shown to be one half of the area of a parallelogram with the same base and height Theorem The area of a triangle is equal to one-half the product of a base and the height (or altitude) for that base. where b is the length of the base and h is the altitude.

Example 1 Example 2 Find the area of the triangle 15 cm 10 cm 8 mm

Example 3 Find the base of a triangle with altitude 15 and area 60. (Hint: draw a picture) Example 4 Find the area of a parallelogram whose sides are 14 and 6 and whose acute angle is 60 degrees. (Hint: draw a picture).

Example 5 Find the area of trapezoid (use formulas you learned in this lesson). 12 13 15 18

Summary State in your own words how you can find the area of a parallelogram and a triangle. Homework: worksheet