A Survey of Mathematics Related Topics: Pg. 452, Orange Box:"Perimeters and Areas"

This applet allow the user to test his or her skill at calculating the area and perimeter of a given figure. The user is given a random figure and allowed to enter a value for the area and perimeter. The applet then informs the user whether or not the values are correct. The user may continue guessing until the answers are correct.

Area, the space within a shape, and perimeter, the distance around a shape, are usually expressed with units. Perimeter is given in terms of the units used to measure distance, 3 feet or 6 meters, for example. Area is given in square units such as 16 meters² or 9 feet².

There are two systems of units that are commonly used: standard and metric. Most of America uses the standard system while many other countries use the metric system. Converting standard units to metric units is done by multiplying by a proportionality constant.

Here are the tables of proportionality constants for the units of length.

Standard	to	Metric
1 ft	=	30.48 cm
1 in	=	25.4 mm
1 yd	=	0.914 m
1 mi.	=	1.606 km

Metric	to	Standard
1 km	=	0.621 mi.
1 m	=	1.094 yd
1 cm	=	0.036 ft
1 mm	=	0.039 in

Metric	to	Metric
1 km	=	1000 m
1 m	=	100 cm
1 cm	=	10 mm

Standard	to	Standard
1 mi.	=	1760 yd
1 yd	=	3 ft
1 ft	=	12 in

So, if we were to convert 8500 feet into kilometers, it would look like this:

8500 ft.   1 yd.     1 mi.     1.606 km
        * ------- * -------- * --------  =  2.6 km
           3 ft.    1760 yds.   1 mi. 

Here are the tables of proportionality constants for the units of area.

Metric	to	Standard
1 m2	=	10.464 ft2
1 km2	=	0.386 mi2
1 km2	=	247.105 acre
1 cm2	=	0.155 in2

Standard	to	Metric
1 ft2	=	0.093 m2
1 mi2	=	2.590 km2
1 acre	=	0.0040 km2
1 in2	=	6.452 cm2

Metric	to	Metric
1 m2	=	0.000001 km2
1 km2	=	1000000 m2
1 cm2	=	0.0001 m2
1 m2	=	10000 cm2

Standard	to	Standard
1 ft2	=	144 in2
1 mi2	=	640 acres
1 acre	=	43560 ft2
1 yard2	=	9 ft2

So, if we were to convert 75 feet² into meters², it would look like this:

          0.093 m2 
75 ft.2 * --------  =  6.975 m2
           1 ft.2