In this worksheet, we will practice finding an unknown length or scale factor when the areas are known or finding an unknown area or scale factor when the lengths are known.

**Q2: **

Given the figure shown, determine the area of a similar polygon, , in which .

**Q3: **

Given the graph, determine the area of similar polygon in which .

**Q4: **

Rectangle is similar to rectangle with their sides having a ratio of . If the dimensions of each rectangle are doubled, find the ratio of the areas of the larger rectangles.

- A
- B
- C
- D
- E

**Q7: **

is a square where , , , and are divided by the points , , , and , respectively, by the ratio of . Find the ratio of the area of to that of .

- A
- B
- C
- D
- E

**Q8: **

In the given figure, is an equilateral triangle with a perimeter of 45 cm. Given that , determine the area of rectangle .

**Q9: **

Using the figure below, find the ratio between the area of the parallelogram and the area of the triangle in its simplest form.

- A
- B
- C
- D
- E

**Q10: **

Given that and the area of , find the area of trapezium .

**Q11: **

If and , find .

- A
- B
- C
- D

**Q12: **

is a parallelogram with and . Let be a point on ray but not on the segment , with . Let be a point on ray but not on the segment , with . Let be a point so that is a parallelogram. If the area of is 39, what is the area of ?

- A9.75
- B78
- C19.5
- D156
- E180

**Q13: **

Triangle is right angled at , where and . Suppose , , and are similar polygons on corresponding sides , , and . If the area of is 145, what are the areas of and to the nearest hundredth?

- A area of , area of
- B area of , area of
- C area of , area of
- D area of , area of

**Q19: **

Rectangle is similar to rectangle with their sides having a ratio of . If the dimensions of each rectangle are tripled, find the ratio of the areas of the larger rectangles.

- A
- B
- C
- D
- E

**Q20: **

Rectangle is similar to rectangle with their sides having a ratio of . If the dimensions of each rectangle are tripled, find the ratio of the areas of the larger rectangles.

- A
- B
- C
- D
- E

**Q21: **

Rectangle is similar to rectangle with their sides having a ratio of . If the dimensions of each rectangle are doubled, find the ratio of the areas of the larger rectangles.

- A
- B
- C
- D
- E

**Q22: **

Given the figure shown, determine the area of a similar polygon, , in which .