Area and Volume

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Geometric Measurements
Fundamental Tools for Mathematical Modeling
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Geometric Measurements
Perimeter
P e r i m e t e r
A r e a
Area
Volume
V o l u m e
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Geometric Measurements
Perimeter The total linear measurement of the
curved and/or straight lines bounding a plane
area. Area The measurement of 2 Dimensional
planar or curved surfaces expressed in square
units. Volume The amount of space occupied by a
three-dimensional object or region of space,
expressed in cubic units.
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Perimeter
S1
S4
S2
S1 S2 S3 S4 Perimeter
S3
S1 x S2 Area
Volume
Height
Length x Width x Height Volume
Width
Length
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Perimeter
Calculate the Perimeter of a Football Field
From goal line to goal line
S1 S2 S3 S4
300
S1
Perimeter
150
S4
S2
End Zone
End Zone
S3
Goal Lines
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Circumference The Perimeter of a Circle
Radius 0.250
a
D
Diameter 2R 0.500
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Calculating the Perimeter of a Triangle
Note Segment ba is congruent to segment bc and
segment da is congruent to segment dc. That
information is given in the figure.
S1
b
S1
S2

4.0
S3
S1
5.0
Perimeter
d
c
a
3.0
6.0
S1
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AREA
Calculate the Playing Area of a Football Field
From goal line to goal line
300
S1
150
S2
End Zone
End Zone
Note 1 acre 43,560 square foot
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The Area of a Circle
Note This is a small circle with a radius equal
to that of the corner radius of the GEARS-IDS 6x9
Plate.
Radius 0.250
a
D
Diameter 2R 0.500
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Calculating the Area of a Triangle
Note Segment ba is congruent to segment bc and
segment da is congruent to segment dc. That
information is given in the figure.
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Volume
Calculate the Volume of a 2 Snow Covering
From goal line to goal line
Volume is the product of 3 valuesLength, Width
and Depth and is expressed in cubic feet, or ft3
300
S1
150
S2
End Zone
End Zone
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The Volume of a Cylinder
Note This is a very small cylinder. These are
the dimensions of the holes in the GEARS-IDS 6x9
Plate
R 0.095
H 0.090
V(cyl) ? r2
H
R
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Calculate the Perimeter of the 6 x 9 Plate
Corner Radius 0.250
8.688
5.688
Note To solve this problem accurately it is
necessary to calculate the perimeter of the
corners.
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Calculate the Area of the 6 x 9 Plate
Corner Radius 0.250
8.688
Hole Dia. 0.190
5.688
Note A precise solution to this problem requires
breaking the area up into multiple small areas
Dont forget to subtract the area of all the
holes!
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Calculate the Volume of the 6 x 9 Plate
Corner Radius 0.250
8.688
Plate Thickness 0.090
Hole Dia. 0.190
5.688
Note The solution to this problem is dependent
on calculating the area accurately!
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Density Using Volume to Calculate Weight
The DENSITY of a material is expressed as the
weight of the material per unit of volume.
Density Weight / Volume Weight Density x
Volume
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Calculate the Weight of the 6 x 9 Plate
Corner Radius 0.250
8.688
Plate Thickness 0.090
Hole Dia. 0.190
Check your calculations by weighing the plate!
5.688
Note The solution to this problem is dependent
on calculating the Volume accurately!
Density of Al (approximately) 1.56 oz/ in3
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Volume of Solids
Quick Reference Slide
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Perimeter and Area of Basic Shapes
Quick Reference Slide
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Go Forth and Calculate,
The End
For Now