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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:

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 .

Q2:

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

Q3:

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

Q4:

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.

Q5:

Two corresponding sides of two similar polygons have lengths of 54 and 57 centimetres. Given that the area of the smaller polygon is 324 cm^{2}, determine the area of the bigger polygon.

Q6:

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

Q7:

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· .

Q8:

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· .

Q9:

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.

Q10:

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 .

Q11:

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 .

Q12:

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 ?

Q13:

Triangle π΄ π΅ πΆ is right angled at π΄ , where π΄ π΅ = 2 0 and π΄ πΆ = 2 1 . Suppose πΏ , π , and π are similar polygons on corresponding sides π΄ π΅ , π΅ πΆ , and π΄ πΆ . If the area of πΏ is 145, what are the areas of π and π to the nearest hundredth?

Q14:

Two corresponding sides of two similar polygons have lengths of 44 and 76 centimetres. Given that the area of the smaller polygon is 121 cm^{2}, determine the area of the bigger polygon.

Q15:

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 .

Q16:

Q17:

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 .

Q18:

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 .

Q19:

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.

Q20:

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.

Q21:

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.

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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