Area math problem please help?

With your correction, i.e., 240 ft of fencing, the largest area (on a plane) you can enclose is a circle. (The proof of this requires what is known as the calculus of variations.) The area, A, of a circle in terms of its circumference, C, (which is the thing you have) is

A = C²/4π = C²/12.56637... = 14400 ft² / π = 4583.662... ft² = 1600 yd² / π = 509.2958... yd²

In acres (acre = 4840 yd²):

= 0.1052264 acre

Incidentally, the largest rectangle you can make, which is what the other answers all seem fixated on(†), is a square of area

A = (C/4)² = C²/16 = 3600 ft² = 400 yd²

= 0.0826446... acre

† Apologies to Nicky, who got the 'joke' after I began my answer, but before I submitted it!

ADDENDUM:

If you had to form the perimeter into an n-gon, with n fixed, the area is maximized by making it a regular n-gon, and the area will be

A(n) = (C/2)²/(n tan(π/n))

For n=4, a square, n tan(π/n) = 4, and you get that earlier result, A = C²/16 = 3600 ft²

For a regular hexagon, n=6, n tan(π/n) = 2√3 = 3.4641.., and A(6) = 4156.922 ft²

For a regular octagon, n=8, n tan(π/n) = 8(√2 - 1) = 3.3137.., and A(8) = 4345.584 ft²

In the limit as n→∞, n tan(π/n) → π, and A(∞) = C²/4π = 4583.662... ft²

Fencing usually does not come by the acre as acres are a unit of measure for area, not length. If my assumption that you meant 240 feet instead of 240 acres, then:

In a square, 60 x 60, which gives a maximum enclosed area of 3600 square feet

If you have 240 feet of fencing : The most area you can get is too arrange the fences in a square: A square, all sides would have 60 feet of fencing. The inside of that would be 3600 feet squared (60 * 60). A rectangle could have sides that are 20 and 100 so that would be 2000 square feet, but 3600 is more and any other way you put it 3600 is the most area.

3600 Square feet is the most area

and the arrangment is a square.

if the width is x and length is y then

2x+2y = 240 => y = 120-x

and the area is

A = x*y = x(120-x) = 120x-x^2

setting the first derivative to zero gives a local maximum or minimum of

120 - 2x = 0 => x = 60

and the second derivative is -2 so the curve is concave downward everywhere. That means that x = 60 is a maximum and the answer is

x = y = 60

A = 3600

ADDENDUM:

LOL after reading the other posts I realize I was superimposing questions I was asked in precalc and assuming a rectangular shape. Shame on me for falling for this. 8)

The triangle has factors, 4, 5, and 3, its 4 by way of fact the middle merchandise is a rectangle, and the choice ingredient is 4. The diameter of the circle is 8, making the radius 4. area of a circle = pi*rsquared, 4 squared is sixteen, circumstances pi = area of your circle, divide that via 2, and you get the area of 0.5 the circle. or 8pi units, you're able to try this math. area of a triangle is .5bh, base is 3, top is 4, 3*4 is 12, divided via 2 (circumstances .5) is 6, the area if the rectangle is BH, or 8*4, wich is 32, so the respond is 32+6+(6pi) or 38+6pi, 3.14*6 = 18.80 4 + 38 = fifty six.80 4, and thats your answer, wish you have been in a position to persist with alongside, im no longer a robust instructor, take the cake in math type although =] perimiter is in basic terms all outdoors factors of the parent, or: .5Dpi of circle, 4, 8, 5, 3. Diameter of the circle is 8, circumstances pi = 25.12, divided via 2 (0.5 circle) is 12.fifty six +4+8+5+3 = 32.fifty six so area = fifty six.80 4 cm squared and perimeter is 32.fifty six cm

An acre is already an area - 4046.85642m^2 - So your question doesn't make much sense...

Aww, come on. The greatest area enclosed by a perimiter of a specified length is achieved by a circle having that circumference, not a square!