Similarity of polygons - Examples, Exercises and Solutions

Look at the two similar rectangles below and calculate the perimeter of the larger rectangle.

Let's remember that in a rectangle there are two pairs of parallel and equal sides.

We will call the small triangle 1 and the large triangle 2.

We calculate the perimeter of the small triangle:

$P_1=2\times3.5+2\times1.5=10$Since we know that the rectangles are similar:

$\frac{3.5}{14}=\frac{p_1}{p_2}$

We place the data we know for the perimeter:

$\frac{3.5}{14}=\frac{10}{p_2}$

$\frac{3.5}{14}\times p_{_2}=10$

$p_2=10\times\frac{14}{3.5}$

$P_2=40$

40 cm

The two parallelograms above are similar. The ratio between their sides is 3:4.

What is the ratio between the the areas of the parallelograms?

The square of the ratio between the sides is equal to the ratio between the areas of the parallelograms:

$3^2:4^2=9:16$

9:16

Is rectangle ABCD similar to rectangle EFGH?

We first need to verify the ratio of similarity.

We examine if:

$\frac{AB}{EF}=\frac{AC}{EG}$

To do this, we substitute our values in:

$\frac{7}{10}=\frac{3}{6}$

$\frac{7}{10}\ne\frac{1}{2}$

The ratio is not equal, therefore the rectangles are not similar.

No

In front of you are two hexagons with a similarity ratio. Which angles are corresponding?

Angle C = Angle O

Which shapes are similar?

The rectangles are similar.

Which figure shows a pair of similar polygons?

Which statement is true?

It cannot be determined.

The polygons below are similar.

Calculate X.

2

Calculate the length of AB given that the triangles below are similar.

4.8

Two similar rectangles are shown below.

What is the height of rectangle number 1?

1.5

Calculate X given that the polygons shown below are similar.

2

ABCD is similar to EFGH.

If the perimeter of ABCD is 54 m, then what is the perimeter of EFGH?

36 m

The two polygons below are similar.

Calculate the missing sides of the polygon ABCD.

5

The price of a square rug that is 2 meters long is $600.

What is the price of a square rug that has a side length of 3 meters?

$1350

Fatima receives $350 for her work on a garden that measures 10 meters by 10 meters.

How much will she receive for working on a garden measuring 20 meters by 20 meters?

$1400