Area Of A Rectangle

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A rectangle is simply a quadrilateral figure that has two sides with equal lengths and other two sides with equal widths and it contains four right angles. The area of a rectangle can be obtained by multiplying the length with the width. There are different ways you can do depending on what kind of information of figures you are provided with. Before we see how we can calculate the area of a rectangles, let’s talk about the basics.

This is how a rectangle looks.

First, a rectangle, has we have said is a quadrilateral meaning that it has four sides. The opposite sides have equal lengths and this means that the sides along the length are equal while those along the width are also equal. For example, if one side of a rectangles is 10 cm, it also means the opposite side is also 10 cm.  Another thing is that a square is also a rectangle, but you will find that not all rectangles can be said to be squares. Just the same way you would find the area of a rectangle, so would you find the area of a square. 

Finding The Area of a Rectangle – What’s the Equation?

If you want to get the area of a rectangle, you use this equation:

Area = Length x Width

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This means that in determining the area of a rectangle, you multiply the length with the width.

Let’s take for example, you are given the length as 5 cm and the width as 4 cm. Now you want to calculate the area of the rectangle.

You write down the equation or formula for finding the area of a rectangle.

Area = Length x Width

Area = 5 cm x 4 cm

Area = 20 cm2

So, your answer will be 20 cm2 or 20 cm.sq.

Sometimes, you may not be given the figures for the length or the width and what you have it the figure for one side and the figure for the diagonal. The diagonal is a line that cuts the rectangle through opposite angles. 

Finding the Area When Given One Side and the Diagonal

If you know the length as well as the diagonal and you are not given the width, you can find the area of the rectangle. In this case, you will need to use the Pythagorean theorem in order to find the width.

The Pythagorean theorem is mostly used to find a third side within a right angled triangle if you have figures for the other two sides. For example, you can use Pythagorean theorem to find the hypotenuse of a triangle. The hypotenuse is the longest side or the width or the length that meet at right angle. Because a rectangle has four right angles, if you draw a diagonal, it will cut through to create a right triangle. When you have the right triangle, you can now apply the Pythagorean theorem.

Pythagorean theorem states that a2 + b2  = c– in this case, a and b represent the sides of the triangle while c represents the longest side or the hypotenuse.

Let’s say that a rectangle has a width of 6 cm and a diagonal of 8 cm. In this case, you will use 6 cm as the value of one side, and then use b as the unknown value of the other side, and then take 10 cm to represent the value for the hypotenuse.

Using the Pythagorean theorem, you can get the value of b.

a2 + b2  = c

62 + b2  = 82

b2 = 82 – 62

b2 = 64 – 36

b2  =  28

b = √28

b = 5.29 cm

So, the length or value for the other side of your triangle and which also represents the other side of your rectangle is 5.29 cm.

Now that you have determined the unknown value of the other side of your rectangle, you can now be able to calculate the area.

Using the equation; Area = Length x Width

Area = 6 cm x 5.29 cm

Area = 31.74 cm2

Note: Area is usually expressed in square meters so you cannot give the value in meters or just centimeters. If you have a drawing that looks like a rectangle but its sides are different and no two opposite sides are equal in their lengths, then that cannot be said to be a rectangle. It may be a trapezoid or an irregular meaning that you may want to use a different formula.

Sometimes, you may be given the area, and the width and you are required to find the length, you can use the equation to get the value. Take for example, the area of a rectangle is 64 cm2 and the width is 6 cm, how do you find the length?

Using the equation; Area = Length x width

So, 64 = a x 6, where a represents the length.

64 = 6a

a = 64 divide by 6

a = 10.67 cm

Therefore, the length of a rectangle whose area is 64 cm2 and the width is 6 cm will be 10.67 cm.

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