1. Area Formulas

2. What is the area formula?
Rectangle
What is the area formula?

3. What is the area formula?
Rectangle
What is the area formula?
b  h

4. What is the area formula?
Rectangle
What is the area formula?
bh
What other shape has 4 right angles?

5. What is the area formula?
Rectangle
What is the area formula?
bh
Square!
What other shape has 4 right angles?

6. What is the area formula?
Rectangle
What is the area formula?
bh
Square!
What other shape has 4 right angles?
Can we use the same
area formula?

7. What is the area formula?
Rectangle
What is the area formula?
bh
Square!
What other shape has 4 right angles?
Can we use the same
area formula?
Yes

8. Practice!
17m
Rectangle
10m
Square
14cm

9. Answers
17m
Rectangle
10m
170 m2
Square
196 cm2
14cm

10. So then what happens if we cut a rectangle in half?
What shape is made?

11. So then what happens if we cut a rectangle in half?
Triangle
So then what happens if we cut a rectangle in half?
What shape is made?

12. So then what happens if we cut a rectangle in half?
Triangle
So then what happens if we cut a rectangle in half?
What shape is made?
2 Triangles

13. Triangle So then what happens if we cut a rectangle in half?
What shape is made?
2 Triangles
So then what happens to the formula?

14. Triangle So then what happens if we cut a rectangle in half?
What shape is made?
2 Triangles
So then what happens to the formula?

15. Triangle So then what happens if we cut a rectangle in half?
What shape is made?
2 Triangles
bh
So then what happens to the formula?

16. Triangle So then what happens if we cut a rectangle in half?
What shape is made?
2 Triangles
bh 2
So then what happens to the formula?

17. Practice!
Triangle
8 m
5 m

18. Answers
Triangle
8 m
20 m2
5 m

19. Let’s look at a parallelogram.
What happens if we slice off the slanted parts on the ends?

20. Let’s look at a parallelogram.
What happens if we slice off the slanted parts on the ends?

21. Let’s look at a parallelogram.
What happens if we slice off the slanted parts on the ends?

22. Let’s look at a parallelogram.
What happens if we slice off the slanted parts on the ends?

23. Let’s look at a parallelogram.
What happens if we slice off the slanted parts on the ends?

24. Let’s look at a parallelogram.
What happens if we slice off the slanted parts on the ends?

25. Let’s look at a parallelogram.
What happens if we slice off the slanted parts on the ends?

26. Let’s look at a parallelogram.
What happens if we slice off the slanted parts on the ends?

27. Let’s look at a parallelogram.
What happens if we slice off the slanted parts on the ends?

28. Let’s look at a parallelogram.
What happens if we slice off the slanted parts on the ends?

29. Let’s look at a parallelogram.
What happens if we slice off the slanted parts on the ends?
What will the area formula be now that it is a rectangle?

30. Let’s look at a parallelogram.
What happens if we slice off the slanted parts on the ends?
What will the area formula be now that it is a rectangle?
b  h

31. Parallelogram
Be careful though! The height has to be perpendicular from the base, just like the side of a rectangle!
b  h

32. Parallelogram
Be careful though! The height has to be perpendicular from the base, just like the side of a rectangle!
b  h

33. Parallelogram
Be careful though! The height has to be perpendicular from the base, just like the side of a rectangle!
b  h

34. Let’s try something new with the parallelogram.

35. Let’s try something new with the parallelogram.
Earlier, you saw that you could use two trapezoids to make a parallelogram.

36. Let’s try something new with the parallelogram.
Earlier, you saw that you could use two trapezoids to make a parallelogram.
Let’s try to figure out the formula since we now know the area formula for a parallelogram.

37. Trapezoid

38. Trapezoid

39. Trapezoid
So we see that we are dividing the parallelogram in half. What will that do to the formula?

40. Trapezoid
So we see that we are dividing the parallelogram in half. What will that do to the formula?
b  h

41. Trapezoid
So we see that we are dividing the parallelogram in half. What will that do to the formula?
b  h 2

42. But now there is a problem. What is wrong with the base?
Trapezoid
But now there is a problem.
What is wrong with the base?
b  h 2

43. Trapezoid
So we need to account for the split base, by calling the top base, base 1, and the bottom base, base 2. By adding them together, we get the original base from the parallelogram. The heights are the same, so no problem there.
b  h 2

44. Trapezoid
So we need to account for the split base, by calling the top base, base 1, and the bottom base, base 2. By adding them together, we get the original base from the parallelogram. The heights are the same, so no problem there.
base 2
base 1
base 1
base 2
(b1 + b2)  h 2

45. Practice!
3 m
Trapezoid
5 m
7 m

46. Answers
3 m
Trapezoid
25 m2
5 m
7 m
(3 m + 7 m)  5m 2

47. Summary!
b  h
b  h
(b1 + b2)  h 2 2