MHB Find Area of A Rectangle With Shortcut

[susanto3311]

hi all...

how do you find area of a rectangle, if its perimeter of a rectangle is = 72 cm?

i mean how to easy find it without hard work.

do you have a formula or just tricks similar like..

http://calculus-geometry.hubpages.com/hub/How-to-Find-the-Area-Perimeter-and-Diagonal-of-a-Rectangle

thanks in advance...

susanto

 

[MarkFL]

For a given perimeter, there are an infinite number of rectangles that will have that perimeter. We need more information about the rectangle.

 

[susanto3311]

For a given perimeter, there are an infinite number of rectangles that will have that perimeter. We need more information about the rectangle.

if perimeter of a rectangle is = 72 cm, counting area of a rectangle =...

i need simple formula to calculate it.
possible?

 

[MarkFL]

Well, suppose we let the height $0<h<36$ be a free variable, then the base $b$ is $b=36-h$. Thus the area $A$ is:

$$A=bh=(36-h)h$$

Thus we find:

$$0<A\le324$$

 

[susanto3311]

Well, suppose we let the height $0<h<36$ be a free variable, then the base $b$ is $b=36-h$. Thus the area $A$ is:

$$A=bh=(36-h)h$$

Thus we find:

$$0<A\le324$$

hi Mark, ..

where come from 36 and 324? it's formula?

another way...Find an Area from just the Perimeter (Geometry) (Page 1) / Help Me ! / Math Is Fun Forum

 

[MarkFL]

The sum of the base and the height must be equal to the semi-perimeter, which is 36...half of 72. And the maximum area comes from the base and height being equal. So the upper bound is $18^2=324$.