Geometry

Unit VIUnit Conversions

Before finding the area (and perimeter) of a figure, you must be certain that the units of measure agree for all the lengths used in finding the area. You must know the following unit conversions in the Standard System of measurement. 1 mile = 5,280 feet 1 yard = 3 ft. 1 yard = 36 inches 1 foot = 12 inches To change a larger unit into a smaller unit, you must ___multiply_________________. To change a smaller unit into a larger unit, you must ___divide_________________. Examples: Complete each statement. a) 2.25 yds = __________ in b) 3 ft 8 in = __________ in c) 1 ft 3 in = __________ yds 2.25 𝑦𝑎𝑟𝑑𝑠

1∗

36 h𝑖𝑛𝑐 𝑒𝑠1 𝑦𝑎𝑟𝑑

81 .41744

3 𝑓𝑒𝑒𝑡1

∗12 h𝑖𝑛𝑐 𝑒𝑠

1 𝑓𝑡+8 h𝑖𝑛𝑐

1 𝑓1𝑡 ∗

12 𝑖𝑛1 𝑓𝑡

+3 𝑖𝑛=15∈¿

15 𝑖𝑛1

∗1 yd

36 h𝑖𝑛𝑐 𝑒𝑠=.417

You will also be expected to convert between units in the metric system of measurement. Recall that the

metric system is based on powers of __10___, so that converting between units simply involves __move the

decimal point left (divides) or right (multiply)_______.

The basic unit for measuring length in the metric system is the ___meter___ and different units are obtained by adding one of the following prefixes: prefix kilo- hecto- deka- meter deci- centi- milli- abbreviation k h dk m dc c m To help remember the order of these prefixes, use the phrase _____King Henry Died By Drinking Chocolate Milk__________________________________. Examples: Complete each statement. a) 3.5 m = __________ cm b) 317 mm = __________ dcm c) 3.5 km = __________ hm

350

Move two places to the right Move two places to the Left Move 1 place to the right

3.17 35

Examples: Find the area of each figure. 1. A rectangle with dimensions 4.8 cm 2. and 25 mm.

18 in

6 ft 4 in

45°

6 𝑓𝑡 4 𝑖𝑛=76 𝑖𝑛25𝑚𝑚

4.8𝑐𝑚=48𝑚𝑚

𝐴=𝑙∗𝑤𝐴=48∗25𝐴=1200𝑚𝑚2

𝑎√2=18𝑎=9√2

¿9 √2

𝐴= h𝑏𝐴=76∗9√2𝐴=684√2 𝑖𝑛2

𝑎√2 𝑎

𝑎

3. Round your answer to the nearest 1000th yd 2. 4. A kite with diagonals 1.2 m and 74 cm.

5 yds 8 in

40

5 𝑦𝑑𝑠 8 𝑖𝑛=5 𝑦𝑑𝑠

1∗

36 𝑖𝑛1 𝑦𝑑

+8 𝑖𝑛=188 𝑖𝑛

cos 40=𝑏

188

𝑏

sin 40=h

188

h

h=120.844

𝐴=12h𝑏

𝐴=12∗144.016∗120.844

𝐴=8701.735 𝑖𝑛2

1.2𝑚=120𝑐𝑚

D

A

B

C

120

74

𝐴=12𝑑1𝑑2

𝐴=12(120)(74)

𝐴=4440𝑐𝑚2

¿144.016

h=188∗ sin 40

𝑏=188∗ sin 40

5. 6. Complete each statement. 1 yd 2 = __________ ft 2 1 ft 2 = __________ in 2 1 m 2 = __________ cm 2

10 mm

1.6 cm

8 mm

¿16𝑚𝑚8mm

82+h2=102

h2=36h=6

𝐴=12h(𝑏1+𝑏2)

𝐴=12∗6 (8+16 )

h=6

𝐴=72𝑚𝑚2

1 𝑦 𝑑2=1296 𝑖𝑛2

9

14410,000