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Geometry and Trigonometry / Area and volume Difficulty: Hard

Parallelogram $A B C D$ is similar to parallelogram $P Q R S$ . The length of each side of parallelogram $P Q R S$ is $2$ times the length of its corresponding side of parallelogram $A B C D$ . The area of parallelogram $A B C D$ is $5$ square centimeters. What is the area, in square centimeters, of parallelogram $P Q R S$ ?

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Explanation

Choice C is correct. It’s given that parallelogram $A B C D$ is similar to parallelogram $P Q R S$ . When two parallelograms are similar, if the scale factor between their corresponding side lengths is $k$ , the scale factor between their areas is $k^{2}$ . It’s given that the length of each side of parallelogram $P Q R S$ is $2$ times the length of its corresponding side of parallelogram $A B C D$ , so the scale factor between their corresponding side lengths is $2$ . It follows that the scale factor between their areas is $2 squared$ , or $4$ . It’s given that the area, in square centimeters, of parallelogram $A B C D$ is $5$ . It follows that the area, in square centimeters, of parallelogram $P Q R S$ is $5 left parenthesis 4 right parenthesis$ , or $20$ .

Choice A is incorrect and may result from conceptual or calculation errors.

Choice B is incorrect and may result from conceptual or calculation errors.

Choice D is incorrect and may result from conceptual or calculation errors.