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.
