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What expression in terms of x can be used to represent the area of parallelogram PQRS?

There is a parallelogram PQRS in which the diagonal PR and the diagonal QS bisect each other into two equal parts at right angle . Each part of both the diagonals has a length 5x.

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MrRoyal

Answer:

[tex]Area = \frac{25x^2}{2}[/tex]

Step-by-step explanation:

Given

Shape: Parallelogram

[tex]PR = 5x[/tex]

[tex]QS = 5x[/tex]

[tex]\theta = 90[/tex]

Required

Find the area of the parallelogram

Because we were given the measure of the diagonals, the area is:

[tex]Area = \frac{1}{2} * PR * QS * \sin \theta[/tex]

This gives:

[tex]Area = \frac{1}{2} * 5x * 5x * \sin \ 90[/tex]

[tex]Area = \frac{1}{2} * 5x * 5x * 1[/tex]

[tex]Area = \frac{1}{2} * 25x^2[/tex]

[tex]Area = \frac{25x^2}{2}[/tex]

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