Good Question!!!?

Question

The four sides of the garden are known to be 20, 16, 12 and 10 cms. And it is also known that it has greatest possible area for those sides. Can you find the area? Please also let me know the formula used.

Answer 1

You can use Heron's formula to do the problem.

Let 20, 16, 12 and 10 cms be the four sides of a quadrilateral. Construct a diagonal x such that 10, 20, x and 12, 16, x form a triangle respectively. Then the total area = the sum of the two triangle's area:

A = [s1(s1-10)(s1-20)(s1-x)]^0.5 + [s2(s2-12)(s2-16)(s2-x)]^0.5

where,
s1 = (10+20+x)/2
s2 = (12+16+x)/2

From A' = 0, solve for x. You can find the maximum area.
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Attention:
If the order can be changed, then you need to construct another pair of triangles with sides 10, 12, x and 16, 20, x respectively. In the same way, you can find the maximum area. Pick the bigger one from the two maximum areas.

Answer 2

Hint: Look up Bretschneider's formula
for quadrilaterals in Wikipedia.
Basically, you have to minimise the
square of the cosine of 2 opposite angles.
What that means is that the sum of the
2 opposite angles is 90 degrees.
So, the maximal area is
sqrt( (s-a)(s-b)(s-c)(s-d) ),
where s is the semiperimeter.
Hope that helps!

Answer 3

Vijay...don't let this fool you. Just draw a picture and break it up into squares and triangles...then, just remember the area formulas for squares and triangles and add them up.

Answer 4

Yeah, there's no real formula for it (except triangle and square areas).

Just divide into square and as many triangles as you need.

Answer 5

It's a parallelogram... just look up the equation for one online. I'd give it to you but I don't know it off the top of my head... I probably should though seeing as how I got 104% average in geometry...

Answer 6

Good question.I was thinking it to be easy but its not so.......