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In this lesson, we will learn how to find an unknown length or scale factor when the areas are known or find an unknown area or scale factor when the lengths are known.

Q1:

π΄ π΅ πΆ π· is a parallelogram with π΄ π΅ = 9 and π΅ πΆ = 5 . Let π be a point on ray ο« π΄ π΅ but not on the segment π΄ π΅ , with π΅ π = 1 8 . Let π be a point on ray οͺ πΆ π΅ but not on the segment πΆ π΅ , with π΅ π = 1 0 . Let π be a point so that π π΅ π π is a parallelogram. If the area of π΄ π΅ πΆ π· is 39, what is the area of π π΅ π π ?

Q2:

Given the graph, determine the area of similar polygon π΄ β² π΅ β² πΆ β² π· β² in which π΅ β² πΆ β² = 6 .

Q3:

Two similar polygons have areas of 20 in^{2} and 80 in^{2}. Find the scale factor of the first polygon to the second.

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 cm^{2}, 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 cm^{2}, determine the area of the bigger polygon.

Q6:

Given the following figure, find the area of a similar polygon π΄ β² π΅ β² πΆ β² π· β² in which π΄ β² π΅ β² = 6 .

Q7:

Given the following figure, find the area of a similar polygon π΄ β² π΅ β² πΆ β² π· β² in which π΄ β² π΅ β² = 9 .

Q8:

Q9:

Given the following figure, find the area of a similar polygon π΄ β² π΅ β² πΆ β² π· β² in which π΄ β² π΅ β² = 3 .

Q10:

Given the following figure, find the area of a similar polygon π΄ β² π΅ β² πΆ β² π· β² in which π΄ β² π΅ β² = 2 .

Q11:

Given that π΄ π· π· πΆ = 3 2 and the area of β³ π΄ π΅ πΆ = 6 9 5 c m 2 , find the area of trapezium π· πΆ π΅ πΈ .

Q12:

If β³ π΄ π΅ πΆ βΌ β³ π π π and π΄ π΅ = 9 5 π π , find a r e a o f a r e a o f π π π π΄ π΅ πΆ .

Q13:

π΄ π΅ πΆ π· is a square where π΄ π΅ , π΅ πΆ , πΆ π· , and π· π΄ are divided by the points π , π , π , and πΏ , respectively, by the ratio of 4 βΆ 1 . Find the ratio of the area of π π π πΏ to that of π΄ π΅ πΆ π· .

Q14:

In the given figure, π» π΄ π· is an equilateral triangle with a perimeter of 45 cm. Given that π΄ π· βΆ π΄ π΅ = 3 βΆ 7 , determine the area of rectangle π΄ π΅ πΆ π· .

Q15:

Using the figure below, find the ratio between the area of the parallelogram π π π πΏ and the area of the triangle π΄ π΅ πΆ in its simplest form.

Q16:

Rectangle π π π π is similar to rectangle π½ πΎ πΏ π with their sides having a ratio of 8 βΆ 9 . If the dimensions of each rectangle are doubled, find the ratio of the areas of the larger rectangles.

Q17:

Rectangle π π π π is similar to rectangle π½ πΎ πΏ π with their sides having a ratio of 5 βΆ 3 . If the dimensions of each rectangle are tripled, find the ratio of the areas of the larger rectangles.

Q18:

Rectangle π π π π is similar to rectangle π½ πΎ πΏ π with their sides having a ratio of 9 βΆ 5 . If the dimensions of each rectangle are tripled, find the ratio of the areas of the larger rectangles.

Q19:

Rectangle π π π π is similar to rectangle π½ πΎ πΏ π with their sides having a ratio of 4 βΆ 7 . If the dimensions of each rectangle are doubled, find the ratio of the areas of the larger rectangles.

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?

Q21:

Given the figure shown, determine the area of a similar polygon, π΄ β² π΅ β² πΆ β² , in which π΄ β² π΅ β² = 3 .

Q22:

Given the figure shown, determine the area of a similar polygon, π΄ β² π΅ β² πΆ β² , in which π΄ β² π΅ β² = 6 .

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