# Solve one side of irregular quadrilateral with known area

### Solve one side of irregular quadrilateral with known area

Hi,
I'm trying to determine the formula for a missing length of a known area irregular quadrilateral.

Its a fairly easy one, but i'm about 40 years outside of my math lessons!

It's a land area problem - and I know the area, but don't know the frontage. I know each side.
So the shape is a triangle on a square.

Example:
Left side = (LS) = 18M
Right side = (RS) = 14M
Area = 400 sq M
Unknown is the length of the square (B)?

I know the area of the triangle + area of the square = 400, which is:
400 = ($$\frac{1}{2}$$* B * (LS-RS)) + (B * RS)

But I can't distill that down to an equation! I know the answer in this case is B=25, but I had to test numbers to find it. I'd like an equation for different values.

Many thanks!
Guest

### Re: Solve one side of irregular quadrilateral with known are

Actually, what you give, $$400= \frac{1}{2}B(LS- RS)+ (B)(RS)$$, is an equation! You have already done most of the work. All that remains is to replace "LS" and "RS" with the values you give, LS= 18m, and RS= 14m.

Doing that you get $$400= \frac{1}{2}B(18- 14)+ B(14)= \frac{1}{2}(4)B+ 14B= 2B+ 14B= 16B$$.

So $$B= \frac{400}{16}= 25$$ meters.

HallsofIvy

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