Video Transcript
Find an expression for the area of
the shape below.
There are several ways of
approaching this problem. And one way is to split the shape
into two rectangles. We can do this by drawing a single
vertical or horizontal line on the diagram. And in this question, we will draw
a vertical line, as shown.
We now have two rectangles. And the area of the whole shape
will be the sum of the areas of these two rectangles. We recall that the area of a
rectangle is equal to the product of its side lengths. This means that the area of the
pink rectangle is equal to 15𝑥 multiplied by 15𝑥. This is equal to 225𝑥 squared.
Repeating this process with the
orange rectangle, we have 14𝑥 multiplied by 𝑥, which is equal to 14𝑥 squared. The total area of the shape is
therefore equal to 225𝑥 squared plus 14𝑥 squared.
Next, we recall that two terms are
like terms if they have the same variables raised to the same powers. And as such, we can take out the
shared factor of 𝑥 squared from our two terms, giving us 225 plus 14 multiplied by
𝑥 squared. Since 225 plus 14 is equal to 239,
this simplifies to 239𝑥 squared. We can therefore conclude that the
expression for the area of the shape in this question in its simplest form is 239𝑥
squared.
