Composite Figures and Pricing

Lesson 1: Perimeter and Circumference - Composite Figures and Pricing

   Constructing Knowledge

Sometimes when budgeting for a home project or as part of a job, it is necessary to determine the cost of supplies. In this lesson, we will focus on calculating costs for items involving a perimeter. Remember that to calculate the perimeter of composite figures:

1. Draw and label a diagram (if there isn't one provided).
2. Calculate any missing side lengths and then label them on the diagram.
3. Calculate the total perimeter by adding up all the side lengths.

For a perimeter problem requiring a cost calculation, determine the perimeter, followed by the cost.

Material costs are often given as unit rates, such as the cost per 12 ft board or cost per package of trim.

Here are a few things to keep in mind:

• Can a portion of the item be purchased or does the entire item need to be purchased? (for example, if 4.8 boards are needed, can you buy 4.8 or do you need to buy 5?)
• Rounding down for the calculated number often will not work (for example, if 4.2 boards are needed you can't round down to 4 boards. You will need 5 boards.)

When solving problems involving real life situations, research whether an item can be bought in parts of a whole or ask your teacher.

   Multimedia

A video showing the solution to a perimeter and pricing problem is provided.

EXAMPLE 1

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Solution

This question has multiple parts. First, a perimeter needs to be calculated, and then the cost needs to be calculated.

Part One: Calculating the perimeter

Step 1: Draw and label the diagram.

In this example, not all of the information from the question is labelled on the diagram. It is also helpful to name each of the sides to help organize the work that needs to be done. Also, the width of the flower bed is given in inches, which will be changed to feet to keep all units the same.

There are 12 inches in 1 foot. Convert 96 inches to feet.

\(\text{number of feet}=\frac{96\,\text{inches}}{12\,\text{inches/foot}}=8\,\text{ft}\)



Step 2: Calculate any missing side lengths and then label them on the diagram.

From the diagram, sides c, d, and e need to be calculated.

Sides c and e are the same length, only one calculation needs to be done. Because the flower bed is 8 feet wide, the length of c and e is 8 feet shorter than a and g.

sides c and e	= 30 ft - 8 ft
	= 22 ft

Side d can be calculated by taking side h and subtracting sides b and f.

side d	= 35 ft - 8 ft - 8 ft
	= 19 ft

The diagram can now be labelled as follows:



Step 3: Calculate the total perimeter by adding up all the side lengths.

Perimeter of flower bed	= a + b + c + d + e + f + g + h
	= 30 ft + 8 ft + 22 ft + 19 ft + 22 ft + 8 ft + 30 ft + 35 ft
	= 174 ft

The perimeter of the garden is 174 ft long.

Part Two: Calculating the Cost of the Railway Ties

Step 1: Calculate the number of Boards needed.

The question states that there will be 2 layers of railway ties, so we need to multiply the original perimeter by 2.

two layers of ties	= 174 ft × 2
	= 348 ft

Each board is 8 feet long, so divide the total number of feet needed by 8.

\(\begin{align} \text{number of ties}&=\frac{348\,\text{feet}}{8\,\text{feet/tie}} \\ \\ &=43.5 \\ \end{align}\)

44 railway ties are needed. (we cannot purchase the ties in shorter lengths so have to round up to 44)

Step 2: Calculate the cost of the 44 railway ties

cost of ties	= 44 ties × $12.75/ties
	= $561.00

The cost of the railway ties for this flower garden will be $561.00.




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