Areas of Similar 2-D Shapes
ex1/ Chris is a travel agent. Recently Chris traveled around Asia. He has decided to enlarge one of his photos for a travel
poster. The original photo is a high quality 4in by 6in. Chris wants the poster to be 20in by 30in.
a) What scale factor is Chris using? k =
=
a scale factor greater than 1
makes sense, since this is an
enlargement
=5
*Because the width is also 5 times larger the shapes are similar.
b) What is the area of the original photo? 4in x 6in = 24in2
Notice that the
dimensions were k times
bigger and the area was
c) What is the area of the new poster? 20in x 30in = 600in2
2
k times bigger
d) How many times bigger is the area of the poster? 600 ÷ 24 = 25 times bigger
Short Overview :
To get the dimensions of the new, similar, 2D shape the original dimensions are multiplied by k. To get the area of the
new, similar 2D shape, the original area is multiplied by k2.
Asimilar = ( k2)(Aoriginal)
ex2/ Jasmine is making a kite from a 2:25 scale diagram. The area of the scale diagram is 20cm2. What will be the area of the
actual kite?
k=
The actual kite's dimensions will be
12.5 times larger and the area will be
(12.5)2 times larger.
= 12.5
area of kite = (12.5) 2 (20cm2)
area of kite = 3125cm2
ex3/ Chris is making a stop sign for his son's play cars that is
the original size. If the area of an actual stop sign is 483in2,
what is the area of Chris's stop sign?
= 4.83in2
ex 4/ Jim’s laptop has a monitor with the dimensions 9 in. by 12 in. The image on his laptop is projected onto the screen of a
whiteboard. According to the documentation for the whiteboard, its screen area is 2836.6875 in2. If the projected screen is
similar, what was the scale factor?
(original area)(k2) = new area
k2 =
(9in x 12in)(k2) = 2836.6875in2
k2 = 26.2656
(108in2)(k2) = 2836.6875in2
k = 5.125
Surface Areas and Volumes of Similar 3-D and Shapes
Ex 1/ Toni created a larger than life model of a Lego block, by enlarging it by a factor of 89. Fill in the dimensions on his new
larger than life Lego block.
a) What was the surface area of the original?
2(w)(h) + 2(w)(L) + 2(h)(L)
2(1)(1) + 2(1)(2)+2(1)(2)
10in2
b) What is the surface area of the model?
2(89)(89) + 2(89)(178) + 2(89)(178)
which happens to
be 10 multiplied by
2
89
79210in2
c) What is the volume of the original?
(L)(w)(h)
(2)(1)(1)
2in3
d) What is the volume of the model?
(178)(89)(89)
which happens to
be 2 multiplied by
3
89
1409938in3
Short Overview :
To get the dimensions of a new, similar, 3D shape the original dimensions are multiplied by k.
To get the new surface area the original surface area can be multiplied by k2.
To get the new volume the original volume is multiplied by k3.
SAsimilar = (k2)(SAoriginal)
Practice Questions:
p. 487-489 #3, 4, 5, 13
p. 497 #1
p. 508 #1, 2, 4, 6
Vsimilar = (k3)(Voriginal)