Table of Contents

- 1 What is the ratio of the perimeter of two similar polygons?
- 2 How are the perimeters and areas of similar polygons related to the ratios of their corresponding side lengths?
- 3 What is ratio of area?
- 4 Is the perimeter of two similar polygons the same?
- 5 What is the ratio of the perimeters in a hexagon?
- 6 Which is half the perimeter of the Pentagon?

## What is the ratio of the perimeter of two similar polygons?

The ratio of the perimeters of two similar polygons is equal to the ratio of the corresponding sides.

Similar polygons are polygons whose ratio of the perimeters is equal to the scale factors of the two polygons. The area ratio of two similar polygons is equal to the square of the proportion of any two corresponding sides and two corresponding diagonals.

**How do you find the perimeter of a similarity?**

Note: The ratios of corresponding sides of the two triangles are in equal if they are similar. The perimeter of the triangle is equal to the sum of their sides.

### What is ratio of area?

In two similar triangles, the ratio of their areas is the square of the ratio of their sides. As can be seen in Similar Triangles – ratios of parts, the perimeter, sides, altitudes and medians are all in the same ratio. Therefore, the area ratio will be the square of any of these ratios too.

### Is the perimeter of two similar polygons the same?

Perimeters of Two Similar Figures : If two polygons are similar, then the ratio of their perimeters is the same as the ratio of the lengths of their corresponding sides.

**Which is the ratio of the perimeters and the areas?**

Ratio of the perimeters : The ratio of the lengths of corresponding sides in the hexagon is = 3 / 9 = 1 / 3 = 1 : 3. Hence, the ratio of the perimeters is also 1 : 3. Ratio of the areas : The ratio of the lengths of the corresponding sides in the pentagons is 1 : 3. Using the Theorem, the ratio of the areas is = 1 2 : 3 2 = 1 : 9. Example 2 :

#### What is the ratio of the perimeters in a hexagon?

Ratio of the perimeters : The ratio of the lengths of corresponding sides in the hexagon is = 3 / 9 = 1 / 3

#### Which is half the perimeter of the Pentagon?

(a) Find the ratio (red to blue) of the areas of the pentagons. Because the ratio of the lengths of the corresponding sides is 1 : 2, the ratio of the perimeters is also 1 : 2. So, the perimeter of pentagon ABCDE is half the perimeter of pentagon LMNPQ. The ratio of the lengths of the corresponding sides in the pentagons is 1 : 2.