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Worksheet: Similar Polygons

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.

Q1:

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

Q2:

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

Q3:

Two similar polygons have areas of 20 in² and 80 in². Find the scale factor of the first polygon to the second.

A
B
C
D
E

Q4:

Two corresponding sides of two similar polygons have lengths of 54 and 57 centimeters. Given that the area of the smaller polygon is 324 cm², determine the area of the bigger polygon.

Q5:

Two corresponding sides of two similar polygons have lengths of 44 and 76 centimeters. Given that the area of the smaller polygon is 121 cm², determine the area of the bigger polygon.

Q6:

Given the following figure, find the area of a similar polygon in which .

Q7:

Given the following figure, find the area of a similar polygon in which .

Q8:

Given the following figure, find the area of a similar polygon in which .

Q9:

Given the following figure, find the area of a similar polygon in which .

Q10:

Given the following figure, find the area of a similar polygon in which .

Q11:

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

Q12:

If and , find .

A
B
C
D

Q13:

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

Q14:

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

Q15:

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

Q16:

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

Q17:

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

Q18:

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

Q19:

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

Q20:

Triangle is right 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

Q21:

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

Q22:

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