1. Parallelograms Lesson 10.3 Areas of Parallelograms and Triangles SWBAT: Develop, state & apply formulas for area of parallelograms and triangles.

2. Area: The number of square units contained in the interior of a figure. Investigate area of a rectangle: What about a square?

3. Draw a diagonal of the rectangle. Cut the rectangle along that diagonal. What new shape(s) are created? How do they compare to each other? How does the area of one of those triangles compare to the area of the original rectangle? Begin with a 3in x 5in note card.

4. Area of a triangle: Where base and height are perpendicular! Sometimes you may need to find the height of a triangle by: ▫P▫Pythagorean Thm ▫4▫45-45-90 or 30-60-90 triangles ▫U▫Using sine, cosine, or tangent!

5. Examples: Find the area of triangle. 1)2) 3) A DCB (two ways) 7 6 4

6. Find the area of the shaded region. 4)5) Area Addition Postulate: The area of a region is the sum of the areas of the non- overlapping parts. *Sometimes the area of a region can be found by finding the difference between two areas. 12 10 25 5 10

7. Begin with a 3in x 5in note card. What is the area of the note card? Why? Label the base (b) and height (h) of the rectangle Draw a segment from one vertex to any point on the opposite base. Cut the rectangle along this segment and move the triangle over to the opposite height. What is the new shape? Has the area been changed?

8. Area of a parallelogram: base: any side of the parallelogram. altitude: (the height) any perpendicular segment between the base and its opposite side. base height base height

9. Examples: Find the area of each parallelogram. 6)7) 45° 20 inches 6 inches 60°

10. Review- Sum of the Interior angles of a polygon with n sides: Each interior angle of a regular polygon: Sum of the Exterior angles of any polygon: Each exterior angle of a regular polygon:

11. 10.3 Assignment State the formula for Area of a rectangle, square, parallelogram, and triangle at the top of your paper. Draw a labeled 30-60-90 and a 45-45-90 triangle at the top of your paper. Ex. 10 – 19, 22 – 24, 36, 37