Question

What is the area?

Answer 1

If all of my assumptions are correct, the area should be 96.72 units.

Explanation:

I made an assumption that `E` is in the very center of the rectangle, such that:

`AE=BE=DE=CE`

Addionally, if `E` is the center of the rectangle:

1. The distance from `AB`'s midpoint to `E` is equal to half of `AD`, since its traveling parallel to `AD` from the edge to the center.
2. The line segment from `AB`'s midpoint to `E` is perpendicular to `AB`

calculated the distance from the midpoint of `bar(AB)` to `E` using Pythagorean's Theorem:

`a^2+b^2=c^2`

`((AB)/2)^2+((AD)/2)^2=(AE)^2`

`sqrt((AE)^2-((AB)/2)^2)=(AD)/2`

`2xxsqrt((AE)^2-((AB)/2)^2)=AD`

Now that we have an equation for `AD`, we can simply multiply it by `AB` to get the area:

`ABxxAD=Area`

`ABxx(2xxsqrt((AE)^2-((AB)/2)^2))=Area`

Next, plug in all of the known terms to calculate the area:

`Area=6xx(2xxsqrt((8.6)^2-((6/2)^2)))`

`Area=12xxsqrt(8.6^2-3^2)`

`Area=12xxsqrt(73.96-9) rArr Area=12xxsqrt(64.96)`

`Area=12xx(8.059776672)=96.71732006`

Finally, we round to two decimal places:

`96.71732006=color(red)(96.72)`