# Worksheet: Areas of 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:

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

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

Q5:

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.

Q6:

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

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 ?

• A78
• B9.75
• C180
• D156
• E19.5

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?

• Aarea of , area of
• Barea of , area of
• Carea of , area of
• Darea of , area of

Q14:

Two corresponding sides of two similar polygons have lengths of 55 and 90 centimeters. Given that the area of the smaller polygon is 121 cm2, determine the area of the bigger polygon.

Q15:

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

Q16:

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

Q17:

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

Q18:

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

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 .

Q23:

A stage for a music festival was built in the shape of an equilateral triangle with an area of 117 m2. 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?

Q24:

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 trapezium ?