1. Area of a Parallelogram
Area of a Triangle
and
Area of a Parallelogram

2. Polygons
Today we are going to find the Area of Parallelograms and the Area of Triangles

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

4. Circle the polygons below.
Regular Polygon
Polygon with all sides congruent
and all angles congruent.

5. Polygons 3 4 5 6 Polygons Regular Polygons # of sides Name Picture
Acute
Equilateral
Triangle 4
Quadrilateral
Square 5
Regular
Pentagon
Pentagon 6
Regular
Hexagon
Hexagon

6. 7 8 9 10 Polygons Polygons Regular Polygons # of sides Name Picture
Heptagon 8
Regular
Octagon
Octagon 9
Nonagon 10
Regular
Decagon
Decagon

7. Area of a Rectangle
The area of a rectangle is equal to the base times the height. Also known as length times width.
height
A = bh
(h)
(b)
base
A = bh is the same as A = lw

8. What is the area of the rectangle?
Area of a Rectangle
What is the area of the rectangle? 2
2 in. x 6 12
in.2
6 in.
12 in2 or square inches

9. A= s2 s Area of a Square 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.
A= s2 s
height = s s
base = s

10. What is the area of the square?
Area of a Square
What is the area of the square? 4
4 m. 4 x 16
m.2
4 m.
16 m2 or square meters

11. Watch carefully not to miss it!
Area of a Parallelogram
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!

12. Area of a Parallelogram
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

13. Area of a Parallelogram
Use this information to find the area of a parallelogram h
height = h h b
base = b
A parallelogram has the same area as a rectangle!
What is the formula for area of a parallelogram?

14. Check to see if you got it right.
Area of a Parallelogram
2 cm.
90º
4 cm.
= 8 cm.2
Check to see if you got it right.

15. Cut off the piece at the dotted line.
Area of a Parallelogram
2 cm.
90º
4 cm.
= 8 cm.2
Cut off the piece at the dotted line.

16. Cut off the piece at the dotted line.
Area of a Parallelogram
2 cm.
90º
4 cm.
= 8 cm.2
Cut off the piece at the dotted line.

17. Move this piece to the other side.
Area of a Parallelogram
2 cm.
90º
4 cm.
= 8 cm.2
Move this piece to the other side.

18. Move this piece to the other side.
Area of a Parallelogram
2 cm.
90º
4 cm.
= 8 cm.2
Move this piece to the other side.

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

20. What is the area of this parallelogram?
Area of a Parallelogram
What is the area of this parallelogram? 5
5 cm. x 7 35
cm.2
7 cm.
35 square centimeters or 35 cm.2

21. What is the area of this parallelogram?
Area of a Parallelogram
What is the area of this parallelogram? 5 x 6
5 ft. 30
ft.2
6 ft.
30 square feet or 30 ft.2

22. Watch carefully not to miss it!
Area of a Triangle
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!

23. Area of a Triangle
Given a right triangle
Make a similar triangle,

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

25. We can use the formula for area of a rectangle
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.
height h
base b
What is the formula for the area of a triangle?

26. When we put 2 right triangles together is made a rectangle.
Area of a Triangle
When we put right triangles together is made a rectangle.
Watch what happens when instead we use 2 isosceles triangles.

27. Given an isosceles triangle
Area of a Triangle
Given an isosceles triangle
Make a similar triangle,

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

29. How do you find the area of the parallelogram?
Area of a Triangle
How do you find the area of the parallelogram?
height h
base

30. Area of a Triangle
5 cm
6 cm
3 cm
9 cm

31. Take out your study guide!
Area of a Triangle
The End!
Take out your study guide!

32. Area of a Parallelogram
# 3
To find the area for a parallelogram use what you know about area of a rectangle.
A = base x height
3 in
A = b x h
5 in
A = 5 x 3
= 15 in2

33. Area of a Triangle # 4 A = base x height A = 8 x 6
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.
A = base x height 2
6 m
8 m
A = 8 x 6
= 24 m2 2