Question Video: Relating the Area of a Rectangle to the Area of a Parallelogram | Nagwa Question Video: Relating the Area of a Rectangle to the Area of a Parallelogram | Nagwa

# Question Video: Relating the Area of a Rectangle to the Area of a Parallelogram Mathematics

The figure shows a parallelogram inside a rectangle. Determine the area inside the rectangle that is not occupied by the parallelogram.

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### Video Transcript

The given figure shows a parallelogram inside a rectangle. Determine the area inside the rectangle that is not occupied by the parallelogram.

In order to answer this question, we recall that the area of any rectangle is equal to its base multiplied by its height. The area of a parallelogram is also equal to its base multiplied by its height. This must be the perpendicular height and not the slant height. The base of the rectangle is 72 centimeters. We need to add 42 and 30. This means that the area is equal to 72 multiplied by 28. This is equal to 2016. As the dimensions were in centimeters, the area of the rectangle is 2016 square centimeters.

The parallelogram has a base of 42 centimeters. It has the same height as the rectangle, 28 centimeters. This means that the area is equal to 42 multiplied by 28. This is equal to 1176. Therefore, the area of the parallelogram is equal to 1176 square centimeters.

We need to calculate the area inside the rectangle that is not occupied by the parallelogram. To calculate this area, we need to subtract 1176 from 2016. This is equal to 840. The area that is inside the rectangle that is not occupied by the parallelogram is 840 square centimeters.

An alternative method here would be to consider the two right-angled triangles. These two triangles are congruent, so we could fit them together to make a rectangle. This rectangle has a base of 30 centimeters and a height of 28 centimeters. Therefore, its area is equal to 30 multiplied by 28. Once again, this gives us an answer of 840 square centimeters.

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