#### Area and Volume

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Area and Volume

Geometric
Measurements
Fundamental Tools for Mathematical
Modeling
Geometric Measurements
Area
Geometric Measurements
Area:
The measurement of
planar or curved surfaces
expressed in square units.
AREA
Calculate the Playing Area of a Football Field
From goal line to goal line
Area S1 S 2
300’
Area 300'150'
S1
Area 4500 ft
S2
150’
Note: 1 acre = 43,560 square foot
2
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
Area (Circle ) R
2
Area (Circle ) 3.14 0.025
2
Area (circle ) 3.14 0.0625
Area (circle ) 0.0122in
D
Diameter = 2R = 0.500”
2
= 3.14
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.
b
S2
4.0” S3
1
Area (a, b, c) base height
2
1
Area (a, b, c) 6"4"
2
2
Area (a, b, c) 12in
d
a
6.0”
S1
3.0
”
c
Calculate the Area of the 6” x 9” Plate
Corner Radius =0.250”
8.688”
Hole
Dia.
0.190”
= 3.14
5.688”
Note: A precise solution to this problem requires breaking the
area up into multiple small areas
Don’t forget to subtract the area of all the holes!
The Surface Area of a Cylinder
Parts of a Cylinder = 2 Circles + 1 Rectangle
r
SAcyl 2r 2rh
2
Area of a Circle x 2
Area of a Rectangle with
Circumference as length
h
Length = Circumference
Calculate the Surface Area of a
Gear Head Motor
3.850”
1.367”
2.00” Dia.
1.55”
SAcyl 2r 2rh
2
Perimeter and Area of Basic Shapes
s
Perimeter = 4s or
s
s+s+s+s
Area =
s2
l
2(l+w) or
w
l+w+l+w
A = lw
P = s 1 + s 2 + s3
s
h
P = 2l+2w or
A = ½ bh
b
Quick Reference Slide
r
C = 2r = d
A = r2
Go Forth and Calculate,
The End
For Now