Math and Arithmetic
Algebra
Geometry

# How do you determine the area of a rectangle if you know the perimeter?

123 ###### 2011-03-03 16:14:30

You can't. The perimeter doesn't tell the area. There are an infinite number of

shapes with different dimensions and different areas that all have the same

perimeter.

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## Related Questions It's undefined, because we dont know the shape of the figure. If it's a square, the perimeter is 12.. if its a rectangle the perimeter MIGHT be 20... We cant determine if we dont know the figure. You can find the perimeter of a rectangle if you know its area and the length of one side. Divide the area by the length of the known side and the quotient will be the length of a side perpendicular to the known side, and then multiply the sum of the two sides by two to find the perimeter. No, you can not calculate an area if you know just the perimeter. For example, rectangle with sides of 10 and 20 would have a perimeter of 60 and an area of 200, but a square of sides 15 would have a perimeter of 60 and an area of 225. You need to know more details about the shape than just the perimeter. If you know the area the divide area by length if you know perimeter subtract it by 2xlength and divide by 2 If the only information that you have is ... A) the figure is a rectangle, and B) the perimeter ... then you cannot calculate the area. The area of a rectangle is the length multiplied by the height., The perimeter is twice the length plus twice the height. So, a rectangle with a length of 9 units and a height of 1 unit will have a perimeter of 20 units and an area of 9 square units. Another rectangle with a length of 6 units and a height of 4 units will also have a perimeter of 20 units, but it will have an area of 24 square units. To be able to calculate the area from the perimeter you need to know one of two additional things - either one of the measurements, or the ratio of the height to the length.+++To summarise, you can, IF you know the ratio as mentioned. Then apply that to half the perimeter to find the length and breadth. Perimeter and area have a relationship but the shape of the space and area together determine the perimeter. A circle has the maximum Area for a given perimeter -or- the minimum perimeter for a given area. Area = pi * radius * radius and perimeter = 2*pi * radius for a circle; perimeter = 2* pi * square root of (Area/pi) With regards to square and rectangles the closer a shape is to square the greater the Area for a given perimeter -or- the minimum the perimeter to a given area. Square Area = side * side and periemter = 4 * side So perimeter = 4 * square root (Area) To solve for a rectangle, you must know ONE side to solve as the relationship between the Area and the perimeter is change as the relative size of side1 and side 2 changes. Rectangle Area = side1 * side2 and perimeter = 2 * (side1 + side2) so perimeter = 2 * (Area/side1 + side1) or 2 * (Area/side2 + side2) "Sq.ft." is the area. It's a phrase used by people who actually don't understandthe whole concept. If you know the sq.ft., then you know the area, because they'rethe same thing. But you can't determine the perimeter from knowing the area.  If the only information that you have is ... A) the figure is a rectangle, and B) the perimeter ... then you cannot calculate the area. The area of a rectangle is the length multiplied by the height., The perimeter is twice the length plus twice the height. So, a rectangle with a length of 9 units and a height of 1 until will have a perimeter of 20 units and an area of 9 square units. Another rectangle with a length of 6 units and a height of 4 units will also have a perimeter of 20 units, but it will have an area of 24 square units. To be able to calculate the area from the perimeter you need to know one of two additional things - either one of the measurements, or the ratio of the height to the length. we know,area of rectangle = l * b perimeter= 45*30=1350 cm ^2 you times the length by the width to get the area of any rectangular or square shapes Unlike a square, knowing the perimeter of a trapezoid is not enough to be able to calculate its area. Think of a rectangle with a perimeter of 20cm. One possibility is that it has a length of 8cm and a width of 2cm. This would give and area of 16cm2. However the rectangle could have also had a length of 7cm and a width of 3cm as this would also give a perimeter of 20cm. However this rectangle now has an area of 21cm2. To be able to calculate the area of the trapezoid, you would need to know more about it than just its perimeter.  Perimeter is a unit of length. Area is a unit of area. The two units are not directly convertible.However, the area of a rectangle is length times width, and the perimeter is two times length plus two times width. Given constant perimeter, a square has maximum area, while a very thin rectangle has nearly zero area. (In calculus terms, the limit of the area as length or width goes to zero is zero.)Depending on how you want to name your units, you can always find a rectangle whose perimeter is "larger" than area, but this is a numerical trick that is not valid in any school of thought of mathematics that I know. You would also need to know the area of rectangle, along with the width in order to determine the length of the rectangle. The distance around is called the perimeter. You can't calculate the perimeter from the area, unless you know the shape. For example, a circle, a square, a 2:1 rectangle, a 3:1 rectangle, all have different perimeters for the same area. More information is needed. For the same perimeter, the area will vary, depending on whether you have a circle, a square, a rectangle with a ratio of 2:1, a rectangle with a ratio of 3:1, etc. You must first calculate the width, using the formula for the area of a rectangle (plug in the numbers you know into the formula, and solve for width). Once you know this, you can plug in the numbers in the formula for a rectangle's perimeter. Write the equation for the perimeter of the rectangle. Replace the known length, and then calculate the width. Once you know that, you can multiply length x width to find the area. The area can't exactly be determined here since we don't have enough information about the sides of the rectangles! We only know that the perimeter of the rectangle is 42 cm. Then: P = 2(l + w) where l is the length and w is the width. 42 = 2(l + w) 21 = l + w Solve for either w or l to get... w = 21 - l So by the area of the rectangle, we obtain: A = lw A = l(21 - l) = 21l - l&sup2; So we can't really determine the area of the rectangle. It's just the general form of the rectangle with the perimeter 42 cm. For a start at this question, find out how wide this rectangle must be. area (250) = length (25) x width (???) The area of a rectangle is its length times its width. We should divide the area by the length (25) to get the width. The answer is 10. Then we know that each long side is 25 and each short side is 10. We know that in a rectangle, the long sides are the same length and the short sides are the same width. In order to get the perimeter, we add 25 and 25 and 10 and 10. We get 70. So the perimeter is 70. The formula for the perimeter of a rectangle is: p = 2(l + w) In other words, just add all four sides. You can't calculate the perimeter of the rectangle if you know only the length. The perimeter of square is 4 x length If you have perimeter only divide by 4 to get length and The area of square is length x length If you already have length that is all you need to know Assuming that you want to minimise the perimeter, then use a square. Its side length is, of course, given by the square root of the area. If the shape is a rectangle...We know that the AREA equals BASE x WIDTH ... A equals B*WIf we divide both sides by B we get: W equals A/BWe know that the PERIMETER equals ( 2 x BASE ) + ( 2 x WIDTH ) ... P equals 2B+2WWe can substitute W in the perimeter formula as follows:P equals 2B+2WP equals 2B+(2*A/B)So... if you know the Base and Area, you should now use this new formula to get the Perimeter.

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