Transcript 8.6 Perimeters and Areas of Similar Figures

8.6 Perimeters and Areas of
Similar Figures
(1 card)
Perimeters and Areas of
Similar Figures
a
b

If the similarity ration is

a
The ratio of the perimeters is
b

The ratio of the areas is
, then:
a2
b2
Ex 1:
The trapezoids are Similar

Find the similarity ratio
(of the top shape to the bottom shape)

Find the perimeter ratio
(of the top shape to the bottom shape)

Find the area ratio
(of the top shape to the bottom shape)
9m
6m
Ex 1:
The trapezoids are Similar

Find the similarity ratio
9
3
=
6
2


Find the perimeter ratio
Find the area ratio
9m
6m
Ex 1:
The trapezoids are Similar

Find the similarity ratio
9
3
=
6
2

Find the perimeter ratio
3
2

Find the area ratio
9m
6m
Ex 1:
The trapezoids are Similar

Find the similarity ratio
9
3
=
6
2

Find the perimeter ratio
3
2

Find the area ratio
9
4
9m
6m
Ex 2:

Two similar polygons have
corresponding sides in the ratio of
5:7
What is the ratio of the perimeters?

What is the ratio of the areas?

Ex 2:



Two similar polygons have
corresponding sides in the ratio of
5:7
What is the ratio of the perimeters?
5:7
What is the ratio of the areas?
Ex 2:



Two similar polygons have
corresponding sides in the ratio of
5:7
What is the ratio of the perimeters?
5:7
What is the ratio of the areas?
25:49
Ex 3: The two regular pentagons
are similar

The area of the smaller pentagon is
42.3 square cm. What is the area of
the larger pentagon
4 cm
10 cm
Ex 3: The two regular pentagons
are similar

The area of the smaller pentagon is
42.3 cm. What is the area of the
larger pentagon
Similarity Rat io
10 5
=
4
2
4 cm
10 cm
Ex 3: The two regular pentagons
are similar

The area of the smaller pentagon is
42.3 cm. What is the area of the
larger pentagon
Similarity Rat io
10 5
=
4
2
4 cm
10 cm
Area Ratio
25
4
Ex 3: The two regular pentagons
are similar

The area of the smaller pentagon is
42.3 cm. What is the area of the
larger pentagon
25
x
=
4
4 2.3
4 cm
10 cm
Ex 3: The two regular pentagons
are similar

The area of the smaller pentagon is
42.3 cm. What is the area of the
larger pentagon
25
x
=
4
4 2.3
x = 264.375 cm2
4 cm
10 cm
Ex 4:

The area of two triangles are 75
square meters and 12 square
meters.
What is the similarity ratio

What is the perimeter ratio

Ex 4:



The area of two triangles are 75
square meters and 12 square
meters.
What is the similarity ratio
75/12 = 25/4 (square root)= 5/2
What is the perimeter ratio
Ex 4:



The area of two triangles are 75
square meters and 12 square
meters.
What is the similarity ratio
75/12 = 25/4 (square root) 5/2
What is the perimeter ratio
5/2