Question Video: Finding the Area of a Parallelogram given Its Dimensions Mathematics

Video Transcript

Given that 𝐴𝐵𝐶𝐷 is a parallelogram, and 𝐸𝐹 equals six centimetres, find its area. So we know that 𝐴𝐵𝐶𝐷 is a parallelogram, and that means that this side is parallel to this side, and this side is parallel to this side. And hopefully we all know this formula: the area of a parallelogram is equal to the length of its base times its perpendicular height.

So if we take 𝐴𝐵 as the base of this parallelogram, the base would be sixteen centimetres; then the perpendicular height is gonna be this distance here, 𝐸𝐹. And we know that because 𝐸𝐹 is perpendicular to 𝐷𝐶; that’s what this symbol here means; and because 𝐷𝐶 and 𝐴𝐵 are parallel, 𝐸𝐹 must also be perpendicular to 𝐴𝐵.

Now the question told us that the length of 𝐸𝐹 is six centimetres, so we know that the perpendicular height is six centimetres. This means we can now work out the area. The length of the base was sixteen; the perpendicular height was six. And six times sixteen, well six times ten is sixty, and six times six is thirty-six. Add those two together; you get ninety-six.

And the lengths were in centimetres, so the area are gonna be in square centimetres. So the answer is, the area of the parallelogram is ninety-six square centimetres, or ninety-six cm squared.