Objective:
Attributes and Dimensions
In this lesson you will demonstrate your understanding
of the concepts and relationships among linear dimensions,
perimeter, area, and volume.
If you need to check a word's definition, please go to the glossary by clicking the Vocabulary button
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Attribute
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Area
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Perimeter
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Volume
- Dimension
| To find the perimeter of a polygon or geometric figure,
you find the distance around it. You will add the lengths
of all sides to arrive at the perimeter. When you find
perimeter, you are working with only one dimension
as you measure around the figure. Since you are only
measuring and adding the lengths around the figure,
the units are labeled as one dimension, usually just
cm, ft, yd, mi, or others. The units are NOT squared
or cubed when finding perimeter because you are working
with one dimension. |
To find the area of a rectangle, use the formula,
L x W, where L is the length of the rectangle and
W is the width of the rectangle. When finding the
area of a rectangle, your results will be in the
units of measurement squared. The reason the units
are labeled squared is because you are working
with only two dimensions when working with area,
length and width. This is often represented
as the units of measure squared or to the second
power. For example, 15 cm2 or
it may be written as 15 squared cm. A = lw
For example:
Find the area of a rectangle 20 feet long and
12 feet wide.
A = l x w
A = 20 x 12
A = 240 feet2
|
To find the area of a triangle, you use the
formula, 1/2 x b x h, where b represents the base
of the triangle and where h represents the height
of the triangle. When finding the area of a triangle,
your results will be in the units of measurement
squared. The reason the units are labeled squared
is because you are working with only two dimensions
when working with area, length and width. A
= 1/2 bh
For example:
Find the area of a triangle with a base of 10.2
feet and a height of 3.5 feet.
A = 1/2 bh
A = 1/2 (10.2)(3.5)
A = 1/2 * 35.7
A = 17.85 feet2
|
| The surface area of a figure is the sum of the areas
of its faces. For example to find the surface area
of a shoe box, you would find the area of each of
the 6 faces of the box. You find the surface area
by finding the area of each face and then adding the
6 different areas together. |
One way to find the volume of a rectangle is
to multiply the dimensions, the length, the width,
and the height of the rectangle. Since we find
volume of a rectangle using three dimensions, length,
width, and height, the answer will be in units
cubed. This is often represented as the units of
measure cubed or to the third power. For example,
12 cm3 or
it may be written as 12 cubic cm. You use the following
formula: V = lwh
For example:
Find the volume of a rectangle with the dimensions
of 13.5 cm in height, 21 cm long, and a width of
6.2 cm.
V = lwh
V = 21 x 6.2 x 13.5
V = 130.2 x 13.5
V = 1757.7 cm3
|
| As you work with measurement, always be sure to
determine what units are in your answer and then
label your answer such. For example, don't say that
the area of the rectangle is 20. You want to be sure
to include the units of measure as well. So the area
of the rectangle would be 20 squared feet. Remember
if you are finding area, the units are squared and
if you are finding volume, the units are cubed. |
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