Question Video: Writing Algebraic Expressions for the Areas of Composite Figures Mathematics

Find an expression for the area of the shape shown.

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Video Transcript

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 π‘₯. We know that from the given measures. The length of this rectangle would be 15π‘₯. We multiply 15π‘₯ by three π‘₯. And we get 45π‘₯ 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 π‘₯ squared. π‘₯ times π‘₯ equals π‘₯ squared. And we have two of those. And that means our area will be 45π‘₯ squared minus two π‘₯ squared. The area of our shape is 43π‘₯ 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 π‘₯ squared. And the squares at the bottom also have an area of π‘₯ squared. Remember the width is three π‘₯. And if we take away two π‘₯ from the length, we get a length of 13π‘₯. Three π‘₯ times 13π‘₯ equals 39π‘₯ squared. If you add 39π‘₯ squared and four π‘₯ squared, you again get 43π‘₯ squared.

The expression for the area of this shape can be written as 43π‘₯ squared.

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