In figure below, what is the area of the parallelogram BCEF where ACDF is a rectangle?

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35 {cm}^{2}

45 {cm}^{2}

55 {cm}^{2}

56 {cm}^{2}

answer is A.

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Detailed Solution

Given, a figure of rectangle as,
Question Image

Now, in the figure, it is mentioned that ACDF is a rectangle and so, the side CD is perpendicular to FD.
Then, we can say that it will act as an altitude for the parallelogram BCEF.
Next, the bases AB and DE of the triangles ABF and CDE are equal by the properties of a rectangle and a parallelogram, i.e., as their respective opposite sides are equal.
So, the base length of the parallelogram BCEF will be,
= FD – ED
= 10 – 3
= 7 cm
So, the base of the parallelogram BCEF is 7 cm and its altitude is 5 cm.
Now, as per the formula for the area of a parallelogram, i.e., the product of its base length and its altitude, we have the area of the parallelogram BCEF as,
= base x height
= 7