1. 8.3 – Area, Volume and Surface Area
Area of Plane Regions
Rectangle
Square
Triangle
3 ft
3 ft
2 ft
6 ft
3 ft
4 ft
A = l·w
A = s·s = s2
A = ½ l·w
A = 6·2
A = 32
A = ½ b·h
A = 12 sq ft
A = 9 sq ft
A = ½ ·4·3
A = 6 sq ft

2. 8.3 – Area, Volume and Surface Area
Area of Plane Regions
Triangle
Parallelogram
Trapezoid
8 cm
2 m
3 yd
9 cm
4 m
7 yd
12 cm
A = ½ b·h
A = b·h
A = ½ (b1 + b2)·h
A = ½ ·4·2
A = 7·3
A = ½ (12 + 8)·9
A = 4 sq m
A = 21 sq yd
A = ½ ·20·9
A = 90 sq cm

3. 8.3 – Area, Volume and Surface Area
Calculate the area of the plane region
24 m
18 m
12 m
A = A + A 
A = 12 · 6 +
18·18 
6 m
A = 72 +
324
6 m
A = 396
sq m
24 – 18 =
6 m
18 – 12 =
6 m

4. 8.3 – Area, Volume and Surface Area
Area of Plane Regions
Circle
Exact Area
Approximate Area
A = ·r2
A = 3.14 ·r2 r d
Calculate the area
Exact Area
Approximate Area
A = ·r2
A = 3.14 ·r2 r d
A = 3.14 ·72
A = ·72
A = 49
sq in
A = 3.14 ·49
Diameter = 14 inches
A =
sq in
r = 7 inches

5. 8.3 – Area, Volume and Surface Area
Formulas for Volume and Surface Area

6. 8.3 – Area, Volume and Surface Area
Formulas for Volume and Surface Area

7. 8.3 – Area, Volume and Surface Area
Calculate the volume and surface area of a rectangular box (prism) that is 7 feet long, 3 feet wide and 4 feet high.
V = l·w·h
SA = 2lw + 2wh + 2hl
V = 7·3·4
SA = 2(lw + wh + hl)
V = 21·4
SA = 2(7·3 + 3·4 + 4·7)
V = 84
cu ft
SA = 2( )
SA = 2( )
SA = 2(61)
SA = 122
sq ft

8. 8.3 – Area, Volume and Surface Area
Approximate the volume and surface area of a cylinder that has a radius of 5 inches and height of 9 inches. ( ≈ 3.14)
V =  · r2 · h
SA = 2r2 + 2rh
V = 3.14·52·9
SA = 2·3.14·52 + 2·3.14·5·9
SA = 2·3.14·25 + 2·3.14·45
V = 3.14·25·9
SA = 50· ·3.14
V = 3.14·225
SA = 3.14( )
V = 706.5
cu in
SA = 3.14(140)
SA = 439.6
sq in

9. 8.3 – Area, Volume and Surface Area
Calculate the volume of a square-base pyramid that has a base side measurement of 3 meters and a height of 5.1 meters.
V = (1/3)· b2 · h
V = (1/3)·32·5.1
V = (1/3)·9·5.1
V = 3·5.1
V = 15.3 m3

10. 8.3 – Area, Volume and Surface Area
Approximate the volume of a cone that has a radius of 4 yards and a height of 6 yards. Round the answer to the nearest tenth of a yard. Use 22/7 as the approximation of .
V = (1/3) · r2 · h
V = (1/3)(22/7)·42·6
V = (1/3)(22/7)·16·6
V = (22/7)·16·2
V = (22/7)·32
V = 704/7
V = 100.6
cu yd

11. 8.4 – Linear Measurement
U. S. Units of Length
U. S. Unit Fractions

12. 8.4 – Linear Measurement Conversions Convert 6 feet to inches.
Convert 8 yards to feet.

13. 8.4 – Linear Measurement Conversions
Convert 68 inches to feet and inches.
Convert 5 yards 2 feet to feet.
5 yd 2 ft = = 17 ft

14. 8.4 – Linear Measurement Conversions
Add 5 feet 8 inches to 8 feet 11 inches.
5 feet 8 inches
13 feet 0 inches
8 feet 11 inches
1 feet 7 inches
13 feet 19 inches
14 feet 7 inches

15. 8.4 – Linear Measurement Conversions Multiply 4 feet 7 inches by 4.× 4
2 feet 4 inches
16 feet 28 inches
18 feet 4 inches

16. 8.4 – Linear Measurement Conversions
A carpenter cuts 1 ft 9 in from a board of length 5 ft 8 in. What is the length of the remaining piece.
5 feet 8 inches –
1 feet 9 inches 4 20
5 feet 8 inches –
1 feet 9 inches
3 feet 11 inches
3 ft 11 in

17. 8.4 – Linear Measurement
Metric Units of Length
Metric Unit Fractions

18. 8.4 – Linear Measurement Conversions Convert 2.5 m to millimeters.
Convert 3500 m to km.

19. 8.4 – Linear Measurement Conversions Subtract 21 mm from 6.4 cm. 64
2.1 43
4.3 43 mm
4.3 cm

20. 8.4 – Linear Measurement Conversions
Multiply 18.3 cm by 6.2 and convert the answer to meters.
18.3 ×
6.2
366
1098
11346
113.46 cm

21. 8.4 – Linear Measurement Conversions
A knitted scarf is currently 0.8 m long. If an additional 45 cm is knitted, how long will the scarf be? 80
0.80 + 45 +
0.45
125
1.25
125 cm
1.25 m