shaded area problem

**stevenw10** · September 6th 2012, 05:43 PM

Question: You have a square yard with a side length of x+5. There is a square brick covered patio in the yard with a side length of x. What is the area of the uncovered portion of the yard?
The answer is 10x+25 but how exactly do I explain and show that? Please help

**Prove It** · September 6th 2012, 07:26 PM

Originally Posted by stevenw10

Question: You have a square yard with a side length of x+5. There is a square brick covered patio in the yard with a side length of x. What is the area of the uncovered portion of the yard?
The answer is 10x+25 but how exactly do I explain and show that? Please help

The area of the yard is $\displaystyle \begin{align*} (x + 5)^2 \end{align*}$ . Of that, $\displaystyle \begin{align*} x^2 \end{align*}$ is covered by bricks.

The uncovered part is therefore $\displaystyle \begin{align*} (x + 5)^2 - x^2 \end{align*}$ . Expand and simplify.

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