Area of a rectangle with one side that is inwardly curved?

[FitFORlife]

Hey I need to know the area of a part of my building that is a rectangle but one side happens to curve inward. I measured it out like so. Side A is 35feet, side B is 62feet, side C is 35feet long, and the curved side D is 66feet. I basically walked along side each wall to get these measurements. I really could use some help on this one, thanks in advance.

 

[Deleted member 4993]

Hey I need to know the area of a part of my building that is a rectangle but one side happens to curve inward. I measured it out like so. Side A is 35feet, side B is 62feet, side C is 35feet long, and the curved side D is 66feet. I basically walked along side each wall to get these measurements. I really could use some help on this one, thanks in advance.

Then it is not a rectangle. It is not possible to calculate area from your description.

Do you have a sketch - that you can share?

 

[galactus]

We may be able to get an approximate answer using two formulae.

Assuming the building's arc is circular. It probably is.

We can use \(\displaystyle s=r{\theta}\), where s=66............[1]

And we can try the length of a chord formula, which is \(\displaystyle 62=2rsin(\frac{\theta}{2})\)............[2]

We have two variables with two unknowns.

From [1], we can solve for r and sub into [2]:

\(\displaystyle {\theta}=\frac{66}{r}\)

\(\displaystyle 62=2rsin(\frac{33}{r})\)

\(\displaystyle r\approx 54.22\)

This gives \(\displaystyle {\theta}=1.217 \;\ or \;\ 69.744 \;\ degrees\)

Now use the area of a circular segment formula, \(\displaystyle A=\frac{1}{2}r^{2}({\theta}-sin{\theta})\)

\(\displaystyle \frac{1}{2}(54.22)^{2}(1.217-sin(1.217))=410\)

That is the approximate area of the circular segment portion of the building. Now add this to the area of the rectangle, (62)(35)=2170

\(\displaystyle 2170+410=2580 \;\ ft^{3}\)