Activating Strategy

Your parents will build a new deck on the back of the house like the one shown. What is the deck's perimeter, and how many square feet of wood will they need to buy to build it?

To solve this problem, I know that I will need to determine the area and perimeter of the swimming pool. I notice that the side lengths of the pool have been provided; however, not all the side lengths are provided. So, first, I will work to find the missing side lengths.

Now that I have determined the pool's missing side lengths, I can find its perimeter. To find the perimeter, I need to add the side lengths. So, I will add 9 m + 6 m + 9 m + 14 m + 9 m + 7 m + 9 m + 13 m. When adding these figures together, I get a total perimeter of 76 m.

Now that I have found the perimeter, I can find the pool area. To find the pool's area, I must decompose this composite rectangle into smaller rectangles. Then, I will multiply the length and width of each of the smaller rectangles to get the area of each smaller rectangle. The sum of each of the smaller rectangles will determine the total area of the pool. 

Looking at the pool blueprint, I could decompose this figure in many ways. I could divide it into 2 rectangles by drawing a vertical line or 3 different rectangles by drawing horizontal lines.

I am going to decompose the figure into 2 smaller rectangles. This would be simpler for me to solve since the side lengths of each decomposed rectangle would be provided.

I know that I can find the area of each decomposed rectangle by multiplying the length and width.

For the left rectangle, I will multiply 9 m x 13 m. This figure's area is 117 m² or 117 square meters.

For the right rectangle, I will multiply 9 m x 14 m. This figure's area is 126 m² or 126 square meters.

Now, I need to add the areas for each decomposed figure to find the total area.

So, 126 m² + 117 m² = 243 m², or 243 square meters.

So, going back to the problem, the perimeter of the tiles along the edge of the pool is 76 m, and the area of the pool's bottom surface is 243 m² or 243 square meters.

Guided Practice

Mathematicians, it is your turn to try!

Your parents will build a new deck on the back of the house like the one shown. What is the deck's perimeter, and how many square feet of wood will they need to buy to build it?

Mathematicians: Remember, we can find the area of a composite rectangle by decomposing the figure into smaller rectangles. Find the area of each smaller rectangle and then add the areas of the smaller rectangles together to find the total area. We can solve a composite rectangle's perimeter by adding all the side lengths. This will reveal the total distance around the figure.

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