Area

CD3 M7 - April 11, 2018

LESSON 1

Units of Area

• Area - the number of square units that is equal to the measure of a surface

• The basic unit of area in the metric system is the square meter. A unit of area can be converted to another by looking at how they are related to each other

Conversion of Units of Measurement of Area

1 square kilometer (km^2) = 1000000 square meters (m^2)

1 square kilometer (km^2) = 100 ha

1 hectare (ha) = 10000 square meters (m^2)

1 square meter (m^2) = 100 square decimeters (dm^2)

1 square decimeter (dm^2) = 100 square centimeters (cm^2)

1 square centimeter (cm^2) = 100 square millimeters (mm^2)

The following are units of area not commonly used:

1 square foot (ft^2) = 144 square inches (in^2)

1 square inch (in^2) = 6.4516 square centimeters (cm^2)

1 square meter (m^2) = 9 square feet (ft^2)

• In converting a given unit of measurement to another, always remember to do the following steps:

- Identify the conversion factor from the table of units of measurement

- Express the conversion factor as a ratio such that the unit of measurement to be cancelled out is in the denominator

- Multiply the given unit of measurement by the conversion factor

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LESSON 2

Planar Figures, Solids and Irregular Planar Figures

• In solving for the area of a planar figure, the following formulas are:

- Area of a Triangle = (b x h)/2

where:

b = base of the triangle

h = height of the triangle

- Area of a Square = s^2

where:

s = side of the square

- Area of a Rectangle = l x w

where:

l = length of the longer side

w = length of the shorter side

- Area of a Rhombus = ( d1 x d2 )/ 2

where:

d1 = first diagonal of the Rhombus

d2 = second diagonal of the Rhombus

- Area of a Circle = πr^2

where:

r = radius of the circle

π = 3.14

• When solving for the surface area of a solid, use the following formulas:

- Surface area of a rectangular solid = 2 [( w + h ) + ( h x l ) + ( l x w )]

where:

w = width

d = height

l = length

- Surface area of a cylinder = 2πr^2 + 2πrh

where:

π = 3.14

r = radius

h = height

- Surface area of a cube = 6e^2

where:

e = edge of the cube

• In solving for the area of an irregular planar figure, divide the figure into regular planar figures such as rectangles, squares or triangles. Solve for the area of each regular planar figure and add all the area to get the total area of the irregular planar figure.