What is the area?

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Answer 1 · 2018-03-21T18:16:42

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

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:

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.
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)#