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

# 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 theyβ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 thatβ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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