1. 10.1 Areas of Parallelograms and Triangles
Area of a Rectangle
The area of a rectangle is the product of its base and height.
A = bh

2. Area of a Parallelogram
The area of a parallelogram is the product of a base and the corresponding height.
A = bh

3. Parallelograms A base of a parallelogram can be any one of its sides.
The corresponding altitude is a segment perpendicular to the line containing that base, drawn from the side opposite the base.
The height is the length of an altitude.

4. Finding the Area of a Parallelogram
What is the area of each parallelogram?

5. Finding a Missing Dimension
For parallelogram ABCD, what is DE to the nearest tenth?

6. Area of a Triangle
The area of a triangle is half the product of a base and the corresponding height.

7. Exploratory Challenge

8. Exploratory Challenge

9. Finding the Area of an Irregular Figure
What is the area of the figure?

11. Exercise #1 Rectangles A & B are similar and drawn to scale
Exercise #1 Rectangles A & B are similar and drawn to scale. If the area of rectangle A is 88 mm2 what is the area of rectangle B?

12. Exercise #2 Figures E & F are similar and drawn to scale
Exercise #2 Figures E & F are similar and drawn to scale. If the area of figure E is 120 mm2 what is the area of figure F?

13. Areas of Trapezoids, Rhombi and Kites
Objectives:
1) Find the area of trapezoids.
2) Find the area of rhombi and kites.

14. A = ½ h(b1 + b2) Trapezoids: b1 = base 1 h = height leg leg
Height – distance between the 2 bases.
* Must be 
b2 = base 2
base
base
Area of trapezoid
A = ½ h(b1 + b2)
Height

15. Ex. 1 Find the area of the following trapezoid.
This is the height!!
30in
18in
36in
A = ½ h(b1 + b2)
= ½ (18in)(36in + 20in)
= ½ (18in)(56in)
= 504in2

16. Ex. 2 Find the area of following trapezoid.
This is a Δ
5cm
A = ½ h(b1 + b2)
= ½ (3.5cm)(5cm + 7cm)
= ½ (3.5cm)(12cm)
= 20.8cm2 h 60
7cm
Need to find h first!
Short side = 2cm
h = 2√3
h = 3.5cm

17. Area of a Rhombus or a Kite
4 equal sides.
Diagonals bisect each other.
Diagonals are .
Kite
Adjacent sides are .
No sides //.
Diagonals are .
Area of Kites or Rhombi
A = ½ d1d2
Diagonal One
Diagonal Two

18. Find the Area of the following Kite.4m
A = ½ d1d2
= ½ (6m)(9m)
=27m2 3m 3m 5m

19. Example 4: Find the area of the following rhombus
d1 = 24m
d2 =
15m
12m
18m b
12m
A = ½ d1d2
= ½ (24m)(18m)
= 216m2
15m
a2 + b2 = c2
122 + b2 = 152
144 + b2 = 225
b2 = 81
b = 9

20. What have I learned?? Area of Trapezoid A = ½ h(b1 + b2)
Area of Rhombus or Kite
A = ½ d1d2

21. Chapter 10.3 Areas of Regular Polygons

22. Vocabulary Radius= the distance from the center to a vertex
Apothem= perpendicular distance from the center to a side

23. Area of Regular Polygon
The area of a regular polygon is half the product of the apothem and the perimeter
A = area
a= apothem
p= perimeter
n= # of sides on the polygon
s=length of side

24. In other words
You can always use the area of a triangle and multiply by how many triangles you can have in the polygon

26. To find the side: Divide the apothem by √3 Then double your answer.30 60
120

27. To find the apothem: Divide the side by 2, then multiply by √330 60

28. r
A=πr2 r