Table of Contents

ratio of their perimeters is equal to the ratio of their corresponding side lengths. the ratio of their areas is equal to the square of the ratio of their corresponding side lengths.

### What is the relationship between scale factor and area?

The area of a scaled object will be equal to the scale factor squared. Again, if the scale factor is three, the area of the new object will be nine times, or three squared, the area of the original object. Finally, the volume of a scaled object will be equal to the scale factor cubed.

**How do you find similar areas?**

Similar areas and volumes

- We already know that if two shapes are similar their corresponding sides are in the same ratio and their corresponding angles are equal.
- When calculating a missing area, we need to calculate the Area Scale Factor.
- Area Scale Factor (ASF) = (Linear Scale Factor) 2
- The figures below are similar.

**How do you find the area of two similar rectangles?**

The scale factor between the two rectangles can be found by looking at the length of corresponding sides BD (3) divided by FH (6), which simplifies to 1/2. To find the area of ABCD multiply the area of EFGH (60) by the scale factor squared: (60) x (1/2) x (1/2) = 15. The area of rectangle ABCD is 15 square units.

## How do you find the scale factor of similar figures?

Suppose you have two similar figures , one larger than the other. The scale factor is the ratio of the length of a side of one figure to the length of the corresponding side of the other figure. Here, XYUV=123=4 . So, the scale factor is 4 .

### How do you do similar shapes?

Two figures are said to be similar if they are the same shape. In more mathematical language, two figures are similar if their corresponding angles are congruent , and the ratios of the lengths of their corresponding sides are equal.

**What is area of similar shape?**

We already know that if two shapes are similar their corresponding sides are in the same ratio and their corresponding angles are equal. When calculating a missing area, we need to calculate the Area Scale Factor. Area Scale Factor (ASF) = (Linear Scale Factor) 2.

**How do you find the area of similar figures?**

The ratio of the area of two similar triangles is equal to the square of the ratio of any pair of the corresponding sides of the similar triangles. For example, for any two similar triangles ΔABC and ΔDEF, Area of ΔABC/Area of ΔDEF = (AB)2/(DE)2 = (BC)2/(EF)2 = (AC)2(DF)2.

## What is aa similarity theorem?

In two triangles, if two pairs of corresponding angles are congruent, then the triangles are similar . (Note that if two pairs of corresponding angles are congruent, then it can be shown that all three pairs of corresponding angles are congruent, by the Angle Sum Theorem.)

### What is a similarity statement?

A similarity statement is a statement used in geometry to prove exactly why two shapes have the same shape and are in proportion.

**What are the similarities between area and volume?**

What is the difference between Area and Volume?

Area | Volume |
---|---|

The area is the amount of space occupied by a two-dimensional flat object in a plane. | Volume is defined as the space occupied by a three-dimensional object. |

The unit of area is in square units. | The unit of volume is in cubic units. |