Find Area Formula of Rectangle

In summary, the formula for finding the area of a rectangle is length x width. To find the length and width, you can use a ruler or measuring tape, or use algebra if you know the perimeter and one side length. The area of a rectangle cannot be negative and will be 0 if the length or width is 0. The formula for finding the area of a rectangle is similar to other shapes, but the key difference is the characteristics of perpendicular sides and 90 degree angles in rectangles.
  • #1
mathdad
1,283
1
Let x denote the width of a rectangle with perimeter 30 feet. Find the area of this rectangle.

Let me see.

P = 2L + 2W

30 = 2L + 2x

(30 - 2x) = 2L

(30 - 2x)/2 = L

A = LW

A = [(30 - 2x)/2]x

Correct?

I guess we can simplify a little more.

A = x(15 - x)

Correct?
 
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  • #2
yes ... the length & width of a rectangle sum to half the perimeter

$P = 2(L+W) \implies L+W = \dfrac{P}{2}$
 
  • #3
Good to be right.
 

FAQ: Find Area Formula of Rectangle

What is the formula for finding the area of a rectangle?

The formula for finding the area of a rectangle is length x width. This means that you multiply the length of the rectangle by its width to get the total area.

How do you find the length and width of a rectangle?

To find the length and width of a rectangle, you can use a ruler or measuring tape to measure the sides of the rectangle. Alternatively, if you know the perimeter and one side length of the rectangle, you can solve for the other side using algebra.

Can the area of a rectangle be negative?

No, the area of a rectangle cannot be negative. Area is a measurement of space and cannot have a negative value.

What happens if the length or width of a rectangle is 0?

If the length or width of a rectangle is 0, then the area will also be 0. This is because multiplying 0 by any number will result in 0.

How is the formula for finding the area of a rectangle related to other shapes?

The formula for finding the area of a rectangle is similar to the formula for finding the area of other shapes, such as squares and parallelograms. However, the key difference is that rectangles have two sides that are perpendicular to each other and all angles are 90 degrees, while other shapes may not have these characteristics.

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