Find Diagonal AC: Square and Parallelogram with Area 100

Question

The square ABCD and the parallelogram AFED are shown below.

The area of the parallelogram is equal to 100.

ED = 5

How long is AC?

00:00 Find AC

00:03 Side length according to the given data

00:07 We'll use the formula for calculating parallelogram area (side times side)

00:13 Multiply by AC as it is the external height to the side

00:20 We'll substitute appropriate values according to the given data and solve for AC

00:35 And this is the solution to the question

The area of a parallelogram is equal to the side multiplied by the height, as we know that ED is equal to 5, the area is also given.

We place the data in the following formula:

$S=AC\times ED$

$100=AC\times5$

We divide by 5 the two sections:

$\frac{100}{5}=\frac{5AC}{5}$

$20=AC$

$20$