Geometry Chapter
Introduction
Area
–
area
is the amount of
Units of Measure
– square units
1 sq ft
8 square feet
8 sq ft
Units of Measure
– square units
1,152 square
inches
1sq in
Area Applications
Welding
How much material is needed to make
something?
We need to make 150 of
these triangular braces.
How much flat stock needs
to be ordered?
4.5 ” 4.0
Boyd Welding – 22 gallon
universal tank
How much sheet metal
would it take to make
each tank?
Area Applications
WeldingArea – Applications
*Estimating: Cost to BuildFloors:
Plywood Subfloor
Flooring (tile, carpet, etc) Interior Walls: Sheetrock Paint Exterior Walls: House wrap
Area
Determine Area – Overview of Process
Steps to Solve…
A = S
2A = LW
A = BH
15
in
9
in
7 in
Parallelogra
m
A = BH
A = 15 in(7
in)
A =
105 sq
in
(1) Identify (classify) the shape. (2) Select the appropriate formula. (3) Select length dimensions that are required. (4) Setup formula, then compute your answer.
2
h
b
b
A
1
2Area
Determine Area -
Rectangle
Rectangl
e
Area = Length x
Width
A =
LW
lengt
h
w
id
th
Characteristics4 straight sides
Each pair of opposite sides are equal length.
Each pair of opposite sides are parallel.
Each vertex is 90
Characteristics 4 straight sides
Each pair of opposite sides are equal length.
Each pair of opposite sides are parallel.
Determine Area -
Square
Square
Area = Length x
Width
A = S
2lengt
h
w
id
th
Area = Side x Side
side
si
d
e
Characteristics
4 straight sides
All 4 sides are of equal length. Each pair of opposite sides are parallel.
Each vertex is 90
Characteristics 4 straight sides
All 4 sides are of equal length. Each pair of opposite sides are parallel.
Each vertex is 90
If the sides are all the same length, there shouldn’t be
Determine Area -
Parallelogram
Characteristics
4 straight sides
Each pair of opposite sides are of equal length.
Each pair of opposite sides are parallel. Opposite angles are equal to one
another.
Characteristics 4 straight sides
Each pair of opposite sides are of equal length.
Each pair of opposite sides are parallel. Opposite angles are equal to one
Determine Area -
Parallelogram
base
h
e
ig
h
t
Area = Base x
Height
2
Determine Area -
Triangle
A =
BH
A = 0.5BH
base
h
e
ig
h
Determine Area -
Trapezoid
Ave. of B
1and
B
2Base 2
Base
1
Area = (Ave. of B
1and B
2) x
Height
Heig
ht
62 ft 85 ft 48 ft +2 = 73.5 ft
= 3,528 ft2
x
Characteristics
4 straight sides
One pair of opposite sides are parallel to one another.
Characteristics 4 straight sides
Determine Area -
Trapezoid
base
1h
e
ig
h
t
base
2
2
21
base
height
base
Area
2
2 1
b
h
b
Determine Area - Circle
diame ter
d × d
4
2
diameter
Area
4
2
Homework
Basic Area Computations
Practice Set 5 pages 30-31
Geometry
Cost
1 of 2
Contractor charges $112 per sq ft to
build a new home.
House: Length 53 ft 8 in, Width 28 ft
Price to build this home?
“Foot print” of house
53 ft 8 in
28
ft
Step 1: Area = LW
Area = 53 ft x 28 ft
Area =
1503 sq ft
Step 2: Cost = Total Area x Price
per sq ft
Cost = 1503 sq ft x $112/sq ft
Cost = $168,336
53 ft
12
8
Cost
2 of 2
How many 8” x 8” ceramic tiles
are needed to cover this wall?
What will be the total cost of
the tiles if they are priced at
$1.09 each?
Wall
58”
89”
Step 2:
Area of one
tile
Area = 8” x 8”
Area =
64 sq in
Step 1:
Area of wall
Area = 89” x 58”
Area =
5162 sq in
Step 3:
Quantity of Tile
Qty = Wall area ÷ Tile
Area
Qty = 5162 sq in ÷ 64 sq
in
Qty =
81 tiles
(rounded
up)
Step 4:
Cost = # tiles x cost
per tile
Homework
Area
Applications
Practice Set 6
Area
Complex Shapes
A = LW
Complex Area
1 of 2
Determine the area of this floor plan:
2 4 f t 1 8 f t 31 ft 9 f t 8.5 ft 7 ft A =24 x
8.5
204 sq ft
A =15 x 7
105 sq ft
Complex Area
1 of 2
Determine the area of this floor plan:
2 4 f t 1 8 f t 31 ft 9 f t 8.5 ft 7 ft
204 sq ft
105 sq ft
+ 279 sq ft
Total Area = 588 sq
ft
204 sq ft
105 sq ft
+ 279 sq ft
Total Area = 588 sq
ft
A =24 x 8.5
204 sq ft
A =15 x 7
105 sq ft A =18 x
15.5
279 sq ft
Complex Area
2 of 2
Determine the surface area of this
swimming pool:
21.5 ft
1
1
.3
f
t
Total Area = 343.2 sq ft
21.5 ft 11.3 ft
11.3 ft
Area = 100.2 sq ft
Homework
Complex Area
Practice Set 7
Geometry
Boyd Welding – 22 gallon
universal tank
How much sheet metal
would it take to make
this tank?
Back
Surface Area
Front
Left
Right
Surface Area
•
How much material (
square inches of sheet
metal
) is needed to fabricate a tank built to
these specifications?
17”
Surface Area
17 in
9.5 in
6 in
SA = 102
in
2+102+57+57+161.5+161.5
SA =
641 in
217” x 6” 102 sq in
17” x 6” 102 sq in
9.5” x 6” 57 sq in
9.5” x 6” 57 sq in
17” x 9.5” 161.5 sq
in
Tramont
Storage
Lateral Surface Area
Sides…
Application:
•Paint
•Paneling
• Sheetrock
Homework
Surface Area
Practice Set 8
Page 43, Refer to assignment list
Surface Area
Surface Area
30”
14”
14”
14” 30”
Lateral Surface Area
Tube*
* = open on the ends
Circumferenc e
Surface Area
30” 14” 14” 14” 30”???
”
3.14 ×
14”
43.96”
𝐴
=
𝜋 𝑑
2
4
𝐴=
𝜋
(
14
)
2
4
𝐴
=
𝐿𝑊
𝐴
=
43.96 ×30
𝐴
=
1,318.8
𝑠𝑞𝑖𝑛
𝐴
=
153.86
𝐴
=
153.86
Total Surface Area
1,318.8 sq in 153.86 sq in 153.86 sq in
1,626.52 sq in
