# Lesson Worksheet: Areas of Similar Polygons Mathematics

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.

**Q3: **

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

**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: **

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

**Q9: **

If and , find .

- A
- B
- C
- D

**Q10: **

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 ?

**Q11: **

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?

- Aarea of , area of
- Barea of , area of
- Carea of , area of
- Darea of , area of

**Q21: **

A stage for a music festival was built in the shape of an equilateral triangle with an area of 117 m^{2}. During rehearsals, it was discovered that the stage needed to be smaller so that technical equipment and more music fans could fit into the concert hall. They removed equilateral triangles from each of the corners of the original equilateral triangle, and the stage ended up as a regular hexagon. What was the area of the new hexagonal stage?

**Q22: **

In triangle , let be a point on and a point on . Suppose that and that . If the area of is 48, what is the area of the trapezoid ?

**Q24: **

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

**Q25: **

where and . If the area of , what is the area of ?