1. copyright©amberpasillas2010

2. Today we are going to find the Area of Parallelograms a nd the Area of Triangles

3. Area The number of square units that are needed to cover the surface of a figure. Polygon Any straight-sided closed plane figure.

4. copyright©amberpasillas2010 The area of a rectangle is equal to the base times the height. Also known as length times width. height base (h) (b) A = bh A = bh is the same as A = lw

5. copyright©amberpasillas2010 What is the area of the rectangle ? 2 in. 6 in. 2 6x 12in. 2 12 in 2 or square inches

6. copyright©amberpasillas2010 A square is a special rectangle. Since the base and the height are the same size, we call them sides ( s ) instead of base and height. s height = s s base = s A= s 2

7. copyright©amberpasillas2010 What is the area of the square ? 4 m. 4 4 x 16m. 2 16 m 2 or square meters

8. copyright©amberpasillas2010 Given the formula for area of a rectangle, we are going to use that information to derive the formula for the area of a parallelogram Watch carefully not to miss it!

9. Draw a straight line from the top corner perpendicular to the base Cut that triangle and move it to the other side What shape does it make? Rectangle

10. copyright©amberpasillas2010 What is the formula for area of a parallelogram ? Use this information to find the area of a parallelogram A has the same area as a rectangle! h base = b height = h h b

11. copyright©amberpasillas2010 4 cm. 90º 2 cm. = 8 cm. 2 Check to see if you got it right.

12. copyright©amberpasillas2010 4 cm. 90º 2 cm. = 8 cm. 2 Cut off the piece at the dotted line.

13. copyright©amberpasillas2010 4 cm. 90º 2 cm. = 8 cm. 2 Cut off the piece at the dotted line.

14. copyright©amberpasillas2010 4 cm. 90º 2 cm. = 8 cm. 2 Move this piece to the other side.

15. copyright©amberpasillas2010 4 cm. 90º 2 cm. = 8 cm. 2 Move this piece to the other side.

16. copyright©amberpasillas2010 4 cm. 90º 2 cm. = 8 cm. 2 Now you have a rectangle A = 8 square cm. or 8 cm. 2 Let’s check it with the area of a rectangle. How many squares do you see?

17. copyright©amberpasillas2010 What is the area of this parallelogram ? 7 cm. 5 cm. 5 7 x 35cm. 2 35 square centimeters or 35 cm. 2

18. copyright©amberpasillas2010 What is the area of this parallelogram ? 6 ft. 5 ft. 5 6 x 30ft. 2 30 square feet or 30 ft. 2

19. copyright©amberpasillas2010 Given the formula for area of a rectangle, we are going to use that information to discover the formula for the area of a triangle. Watch carefully not to miss it!

20. Given a right triangle Make a similar triangle,

21. Given a right triangle Make a similar triangle, flip it and put both triangles next to each other What polygon is this? A Rectangle

22. copyright©amberpasillas2010 What is the formula for the area of a triangle ? We can use the formula for area of a rectangle to find the formula for area of a triangle. Two triangles make one rectangle. We want to find half of the area of the rectangle. base height b h

23. When we put 2 right triangles together is made a rectangle. Watch what happens when instead we use 2 isosceles triangles.

24. Given an isosceles triangle Make a similar triangle,

25. Given an isosceles triangle Make a similar triangle, flip it and put both triangles next to each other What polygon is this? A Parallelogram

26. copyright©amberpasillas2010 base height h How do you find the area of the parallelogram?

27. copyright©amberpasillas2010 9 cm 5 cm6 cm 3 cm

28. The End! Take out your study guide!

29. copyright©amberpasillas2010 Area of a Parallelogram # 3 5 in 3 in A = b x h A = 5 x 3 = 15 in 2 To find the area for a parallelogram use what you know about area of a rectangle. A = base x height

30. copyright©amberpasillas2010 # 4 Area of a Triangle 8 m 6 m A = 8 x 6 2 = 24 m 2 A = base x height 2 A triangle is half the area of a rectangle. To find the area of a triangle you use the rectangle formula and divide it in half.