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4.5 E) Area of Rectangles – Part 2
4.5 E) Area of Rectangles – Part 2
We are now going to have a look at working out the area of a rectangle that has a length and a width in terms of unknown values. We have learnt from the previous section that to work out the area of a rectangle, we need to multiply the length by the width. We are going to use exactly the same method here. The only difference is that we will be multiplying unknowns rather than numbers, which makes the maths slightly trickier and it means that we need to be more careful when we are multiplying. If you not very confident with multiplying out unknowns, it is worth going through the algebra section before working through this section (click here to be taken through to the algebra section).
Example 1
What is the area of the rectangle below?
What is the area of the rectangle below?
We work out the area of a rectangle by multiplying the length by the width. The length of the rectangle is 3x and the width of the rectangle is (x + 2). This gives us the calculation below.
I am going to tidy this up by getting rid of the multiply sign.
The next step is to multiply the term that is on the outside of the bracket by all of the terms that are on the inside of the bracket. I am going to use arrows going from the term that is on the outside of the bracket (3x) to all of the terms on the inside of the bracket. This is to ensure that I multiply the 3x by all of the terms inside the bracket.
Therefore, the area for this rectangle is 3x2 + 6x.
Example 2
What is the area of the rectangle below? Make sure that you simplify your answer.
What is the area of the rectangle below? Make sure that you simplify your answer.
To work out the area of this rectangle, we are going to multiply the length by the width. The length of the rectangle is (x + 4) and width of the rectangle is (x – 3). We therefore undertake the following calculation.
I am going to tidy this up by removing the multiply sign that is in the middle.
There are two terms in each of the brackets and the easiest way to multiply these brackets out is to remember FOIL (First, Outside, Inner and Last).
We now need to collect like terms. There are two terms that contain x’s and this means that we are able to combine them; we are able to combine the 4x and the -3x. The simplified area becomes: