Find an expression for the area of the shape shown below.
We can find this expression in a few different ways. Imagine that we treat this shape like a rectangle. The width of this rectangle would be three 𝑥. We know that from the given measures. The length of this rectangle would be 15𝑥. We multiply 15𝑥 by three 𝑥. And we get 45𝑥 squared.
But then, we need to take away these two shaded boxes because they’re not part of our area. The area of this shaded box is 𝑥 squared. 𝑥 times 𝑥 equals 𝑥 squared. And we have two of those. And that means our area will be 45𝑥 squared minus two 𝑥 squared. The area of our shape is 43𝑥 squared.
But that’s not the only way we could find the area. We could break our area up into five pieces. We already know the squares at the top would be 𝑥 squared. And the squares at the bottom also have an area of 𝑥 squared. Remember the width is three 𝑥. And if we take away two 𝑥 from the length, we get a length of 13𝑥. Three 𝑥 times 13𝑥 equals 39𝑥 squared. If you add 39𝑥 squared and four 𝑥 squared, you again get 43𝑥 squared.
The expression for the area of this shape can be written as 43𝑥 squared.