8.1 Areas of Parallelogram s (and rectangles)
Aparallelogram  base  height  bh
Base
H eight
Base
1. Area = _________
11 c m
7 cm
5 cm
2. The figure is a rectangle with perimeter 126 m. Area = _________
38 m
3. The area of the parallelogram is 936 sq ft. h = _________
3 9 ft
h
2 8 ft
1
Deriving the formula
Area= the number of unit squares in an object. (laying tile)
If each squ are is 1 inch by 1 inch,
then w hat is the area of this rectangle?
Area = _____ Colu m ns  ______ Row s =________
Area = Base  H eight
Parallelogram s:
Height
Base
2
3
8.2 Areas of Triangles
Aparallelogram  base  height  bh
Parallelogram :
Atriangle
1.
1
1
 base  height  bh
2
2
The area of the obtuse triangle is 176 sq ft. h = _________
2 7 ft.
h
1 8 ft.
2 2 ft.
4
1
Atrapezoid  hb1  b2 
2
2
h
2
2
1.
2
Area = _________
11 m
13 m
12 m
15 m
25 m
2.
The perimeter is 138 cm and the area is 924 cm2. h = ________
h
27 cm
34 cm
5
Kite
d1 = long diagonal of kite
d2 = short diagonal of kite
Area = (½) d1d2
Review:
d2 is bisected by d1
d2 and are d1 perpendicular
d1 creates two congruent triangles
Use the follow ing to show that Area = (½) d1d2
(Mark each figure with d1 and
1
d2 )
2
A rea of a kite=
Example:
Area of ABCD = _________
6
7
8.3 Applications of Area.
1. Ian w ants to pu t d ow n tile in his kitchen. Each tile is 1 square foot. A picture of his
kitchen is below , each square is a square foot. H ow many tiles d oes Ian need to bu y?
2. Ian now w ants to carpet three rooms. The carpet costs $4 per squ are foot, the
pad d ing costs $3 per squ are foot, and the installation is free. The d im ensions of the
room s are as follow s: Room 1 is 10' X 12', Room 2 is 5' X 2', and Room 3 is 20' X 15'.
H ow much w ill carpeting these three room s cost him ?
8
9
8.4 Areas of regular polygons
(congruent angles and sides)
r
APOTH EM of a regular polygon is a perpend icular bisector segm ent from the center of the polygon's
circum scribed circle to a sid e of the polygon.
Areas of a regular polygon
Aregularpolygon 
1
2
sidelengthapothem# ofsides  1 sa n
2
Aregularpolygon 
Use the follow ing to show that
(Mark each figure with
1
2

sa n
s and a)
In a Reg. Pentagon there are_______________congruent triangles
In a Reg. Octagon there are_______________congruent triangles
In a Reg. N onagon there are_______________congruent triangles
10
1.
Each side of the regular pentagon is 11.9 cm and the apothem is about 8.2 cm. Area  _________
2.
The shaded portion of the regular octagon represents a redwood deck that is to be stained. The apothem is
about 14.5 ft.
Shaded area  _________
1 2 ft
3. The A of a regular polygon is 300 m 2 , the a = 10 m . Find the perim eter of the polygon.
Write the area form ulas for the follow ing.
Area of a Parallelogram :
Area of a Triangle:
Area of a Trap ezoid :
Area of a Kite:
Area of a Regu lar Polygon:
11
12
8.5 AREA OF A CIRCLE
ACircle  r 2
tu rn to pg.454
1. Find the area of the circle w ith rad ius:
a) 4cm
b) 3.56 in
c) 7 m
d ) 56 ft
e) 5 mm
2. The circum ference is 22 m . Find the area. Area  _________
3. Use all of your past areas to find the area of the shad ed regions.
56
10
14
28
a)
b)
10
c)
13
14
8.6 AN Y WAY YOU SLICE IT
Picture of:
Area of:
Sector of a
circle
segment of
a circle
Annulus
Find the area of the shaded regions.
4
2
1.
2. r= 3 cm
3. r= 3 cm . (think of a d ifferent w ay of looking at the triangle)
4. Square of length 4 inches.
15
16
8.7 Surface Area
Cut out the follow ing and fold to m ake a rectangular prism . Find it’s surface area in m m .
Total Su rface Area =
l  Slant height= _________________________________________________
Cu t ou t the follow ing to m ake a squ are based p yram id :
Total Surface Area of the square-based pyram id in m m =
17
1. Find the total su rface area of the trap ezoid al p rism . Measu rem ents are in m eters. Su rface area _________
17
12
15
20
22
42
2.
Total surface Area = __________
Special ones
Picture of lateral surface and base / bases
Lateral Surface Area
Cylinder
Cone
18
2. Surface Area=
3. Find the surface area of a cone w ith
4m
slant height 8 and rad ius 3
15 m
Area of a Parallelogram :
Area of a Triangle:
Area of a Trapezoid :
Area of a Kite:
Area of a Regular Polygon:
Area of a Circle:
Lateral Surface Area of a cone Cone:
Lateral Surface Area of a Cylind er:
19
10. If it costs the $25 for a gallon of paint and a gallon of paint covers 35 square feet. H ow m uch
w ould it cost to paint the pyram id ?
11. Find the surface area of the large pencil.
5 in
IAN PENCIL CO.
Radius =3 inches
14 inches
20