How to Solve Problems with Measurement

Instructor: Lynne Hampson

Lynne Hampson has a Masters in Instr. Design & Bach. in Elem./Spec. Educ. She taught 8 years in Elem. Core, Science, Coding, Microsoft, Internet Safety, and Life Skills.

In this lesson, we will use basic mathematical operations to solve problems involving perimeter, area, and volume. You will also learn a method for scaling to compare models to real structures or objects.

Measurement Problem-Solving

Measurement is the process of using a device or tool to find the dimensions, time, pressure, amount, weight or mass of an object. We use measurements to help us solve problems in many real world situations.

Perimeter and Area

  • To find the perimeter of an object or place, measure the distance around something. Whether the shape is a circle, triangle, rectangle or polygon, the definition of the perimeter is the same. The formula, on the other hand, may vary depending on the shape of the object.
  • Area is defined as the amount of space inside a boundary. The boundary can be a variety of shapes and calculating the area will depend on the shape.

Problems

You have built an amazing tree house, but you want to make it look like a real house. You are ready to install new carpet and baseboard trim. Even though it looks visually square, it is not. Use your knowledge of perimeter and area, and the schematic of the dimensions of the treehouse to calculate the amount of carpet and trim needed.

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First, realize this is a two step problem. Not only are you installing carpet, but the baseboard trim also needs to be nailed to the wall base around the perimeter of the room.

Carpet Area Measurement:

The carpet covers the floor of the room. As you know, this is called the area of the room. Generally, you will multiply one length and one width to find your answer.

In this case, however, the sides are all a little off. The fix for this is quite simple. Since the measurement is quite close, multiply the side with the largest width times the side with the largest length. For this room, the length is 10 ft 3 in. The largest width is 10 ft 2.4 in. Measuring this way, you will have a little excess carpet, but it is better to have a little more than not enough when buying carpet.

Use Conversion to Find the Answer:

Step One:

Both the length and width are 10 feet long.

There are 12 inches in every foot, so 10 ft x 12 in = 120 in

Step Two:

Now, add the extra 3 inches to the length and extra 2.4 inches to the width.

Length: 120 in + 3 in = 123 in

Width: 120 in + 2.4 in = 122.4 in

Step Three:

Multiply your conversions to find the area:

123 in x 122.4 in = 15,055.2 square in

Step Four:

Divide 15,055.2 by 12 inches and by 12 inches again, to convert square inches to square feet.

15,055.2 / 12 / 12 = 104.6 square ft

Measuring the Perimeter

Use the same picture to measure for trim. To find the perimeter of the room take all of the length and width measurements on all sides and add them together.

Step One:

Add the feet, or multiply if you have the same amount of feet on each side.

10 ft x 4 = 40 ft

Step Two:

Add together the inches of all the sides.

2 in + 3 in + 2.5 in + 2.4 in = 9.9 in

Final Answer:

You will need a minimum of 40 ft 9.9 in of board. (However, if you don't want seams in your baseboard you may do well to buy four 12 foot boards.)

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