10.3
Areas of Similar
Shapes
Similarity
Z
N
4
I
6
2
R
3
CORN ~ MAIZ
8
M
4
C
5
10
O
A
List 3 properties of similar shapes:
•Same shape, different size
•Corresponding angles are congruent
•Corresponding sides are proportional
find missing sides
A
B
W
X
6 in
9 in
Z
D
x
C
10 in
Y
ABCD ~ WXYZ
Squares Review
Squares that you should memorize
2
1
2
2
2
3
4
2
5
2
6
2
7
2
8
2
9
2
10
2
2
11
12
2
Connections: sides and Perimeter
A
B
W
X
6 in
9 in
Z
D
15 in
C
Pick two corresponding sides (left
to right). What is the ratio of the
sides? Simplify if needed.
ABCD ~ WXYZ
10 in
Y
What is the ratio of the perimeters
of both shapes (left to right)?
Simplify if needed.
What do you notice about both of these answers?
Connections: sides and Perimeter
C
9 cm
A
3 cm
F
B
6 cm
9 cm
∆ABC ~ ∆DEF
D
Pick two corresponding sides (left
to right). What is the ratio of the
sides? Simplify if needed.
2 cm
6 cm
E
What is the ratio of the perimeters
of both shapes (left to right)?
Simplify if needed.
What do you notice about both of these answers?
Connections: sides and Perimeter
∆BAT ~ ∆MEN
M
B
20 yd
15 yd
12 yd
E
A
25 yd
16 yd
20 yd
N
T
Pick two corresponding sides (left
to right). What is the ratio of the
sides? Simplify if needed.
What is the ratio of the perimeters
of both shapes (left to right)?
Simplify if needed.
What do you notice about both of these answers?
Connections: sides and area
A
B
W
X
6 in
9 in
Z
D
15 in
C
Pick two corresponding sides (left
to right). What is the ratio of the
sides? Simplify if needed.
ABCD ~ WXYZ
10 in
Y
What is the ratio of the areas of
both shapes (left to right)?
Simplify if needed.
What do you notice about both of these answers?
Connections: sides and area
D
I
C
O
DIET ~ COAK
6 in
12 in
K 4 in A
T
8 in
E
Pick two corresponding sides (left
to right). What is the ratio of the
sides? Simplify if needed.
What is the ratio of the area of
both shapes (left to right)?
Simplify if needed.
What do you notice about both of these answers?
Summary
2.
1.
The ratio of the perimeters of two shapes is
_________________________________
_________________________________ .
The ratio of the areas of two shapes is
_________________________________
_________________________________ .
Practice
Practice
Practice
Practice
Practice
Lesson Revisited:
Ratio of Sides
Ratio of Perimeters
Ratio of Areas
6) The hexagons at the right are similar. What is the ratio (smaller to larger)
of their perimeters and their areas?
Ratio of
Sides
Ratio of
Ratio of
Perimeters Areas
Finding the missing perimeter:
The figures in each pair are similar. The perimeter of one figure is given.
7)
Write a proportion:
Ratio of
perimeters
(using sides)
Perimeter of smaller pentagon = 40 m
Ratio of
ACTUAL
perimeters
=
Finding the missing perimeter:
The figures in each pair are similar. The perimeter of one figure is given.
8)
Write a proportion:
Ratio of
perimeters
(using sides)
Perimeter of smaller rectangle = 12 in.
Ratio of
ACTUAL
perimeters
=
Finding the missing area:
The figures in each pair are similar. The perimeter of one figure is given.
Write a proportion:
9)
Ratio of
areas
(simplified)
Area of smaller pentagon = 80 m2
Ratio of
ACTUAL
areas
=
Finding the missing perimeter:
The figures in each pair are similar. The perimeter of one figure is given.
10)
Write a proportion:
Ratio of
areas
(simplified)
Area of smaller rectangle = 8 in2
Ratio of
ACTUAL
areas
=
Going further…
13) The ratio of the areas of two rectangles is 49:36.
a) What is the ratio of the sides?
b) What is the ratio of the perimeters?
14) The ratio of the areas of two rectangles is 32:50.
a) What is the ratio of the sides?
b) What is the ratio of the perimeters?
Ratio of
Sides
a
b
Ratio of
Perimeters
a
b
Ratio of
Areas
a2
b2