10.1 area of polygons 1

1. 10.1 Area of Polygons
Page 521

2. Essential Questions
How do you know when to find
circumference or area?
What strategies and formulas can you
use?
How is surface area used in the real
world?
How is the volume of a pyramid related
to the volume of a box?
How is the volume of a cone related to
the volume of a cylinder?

3. Area and Perimeter
Perimeter-The distance around a polygon
(the sum of the length of all sides)
Area- The number of square units inside a
closed figure

5. Formulas
Triangle: b x h or 1/2bh
2
Rectangle: A = l x w
Square: A = l x w or s
2
Parallelogram: A = b x h
Trapezoid: (b
1
+b
2
) x h or ½ (b
1
+b
2
)x h
2

6. Area
Steps:
1.Write the area formula
2. Substitute the values given
3. Answer

7. Area of a parallelogram
height
base
A = b x h
90º

8. What is the area of this parallelogram?
base 7 cm.
height 5 cm.
A = b x h
A = 5 x 7
A = 35 cm
2
Perimeter
P= 5 + 7 + 5 + 7 = 24 cm

9. What is the area of this parallelogram?
6 ft.
5 ft.
8 ft.
A = b x h
A = 5 x 6
A = 30 ft
2
Perimeter
P= 6 + 8 + 6 + 8 = 28 ft

10. What is the area of this parallelogram?
5 m.10 m.
12 m. A = b x h
A = 10 x 5
A = 50 m
2
Perimeter
P= 5 + 12 + 5 +12= 34 m

11. Area of a trapezoid
•Area =
(b
1
+b
2
) x h
2
base 1
height
base 2

12. Area of a trapezoid
•Area =
(b
1
+b
2
) x h
2
base 1 base 2
height

13. What is the area of this trapezoid?
15 inches
8 Inches
7 inches
•Area =
(b
1
+b
2
) x h
2
A= 88 in. sq.
12
•Area =
(15 +7) x 8
2
Perimeter
P= 7 + 15 + 12 + 12= 46 in

14. GUIDED PRACTICE for Examples 1 and 2
Substitute values for b
1
, b
2
and h.
Multiply.
A = (b
1
+ b
2
)h
1
2
1
2
A =(14 + 17)6
= 93 square feet
Write formula for area of a trapezoid.
2. A trapezoid with bases of 14 feet and 17 feet and a
height of 6 feet

15. What is the area of this trapezoid?
A= 412.5 cm sq.
25
15 20
cm
35
•Area =
(b
1
+b
2
) x h
2
•Area =
(20 +35) x 15
2
Perimeter
P= 35 + 25 + 20 + 25= 105 cm

16. How to find the area of a square
or rectangle.
3 cm.
5 cm.
Step 1 – Multiply the length times the
width. (A = l x w)
5
3x
15cm
2
Perimeter
P= 3 + 5 + 3 + 5= 16 cm

17. What is the area?
2 in.
6 in.
2
6x
12in.
2
A = b x h
Perimeter
P= 2 + 6 + 2 + 6 = 16 in

18. TRIANGLES
Area formula for triangles is
A = b x h or ½ b (h)
 2
h
b

19. What is the area of this triangle?
20 in
20 in
Area = b x h
2
A= 200 in. sq.
Area = 20 x 20
2

20. What is the area of this triangle?
5 in
10 in
Area = b x h
2
A= 25 in. sq.
Area = 5 x 10
2

21. What is the area of this triangle?
10 in
8 in
Area = b x h
2
A= 40 in. sq.
Area = 10 x 8
2

22. Find the area and perimeter:
9 cm
18 cm
12 cm
8
9 cm
18 cm
12 cm
A= 72 cm sq. P= 9 + 12 + 18 = 39 cm
Area = b x h
2
Area = 18 x 8
2

23. Find the area and perimeter:
10 in
15 in
7 in
8 in
A= 28 in. sq.
P= 10 + 15 + 7 = 32 in.
Area = b x h
2
Area = 8 x 7
2