Properties, Characteristics and proofs: Parallelogram within a square

Look at the square below:

Is AF equal to ED?

Since it is not given that FD is parallel to AE, it cannot be argued that AF is necessarily equal to ED

No

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?

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:

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

$20=AC$

$20$

Square ABCD and parallelogram AFED are shown below.

Is side AE a bisector?

No

In the square ABCD, side FD is parallel to side AE.

Is AF equal to ED?

Yes

The parallelogram AFED is drawn inside the square ABCD.

Are the areas of triangles ACE and FBD equal?

Yes

Square ABCD and parallelogram AFED are shown below.

The area of the parallelogram is equal to 64.

$AF=4$

How long is side AC?

$16$

Square ABCD and parallelogram AFED are shown below.

Parallelogram AFED has an area equal to 4.

$AC=4$

How long is side ED?

$1$