Perimeter and area are two math concepts that students often get confused. Perimeter is the distance around an object or surface. For instance, fences often go around the perimeter of a backyard, playground or garden. On the other hand, area is the amount of space inside of a given surface. Painting a house or installing carpet requires knowledge of the area.

## Objective

Students will be able to distinguish between and calculate perimeter and area. Additionally, they will know the circumstances to use the formula for area or perimeter to solve a problem.

## Hook

Take students outside and have them stand on the line of any court. A four square court is good for smaller classes while half of basketball court may be better for larger classes. Explain that the class represents the perimeter of the court. The perimeter is the distance around. To find the perimeter one needs to measure the length and the width. Give two students a measuring tape and have them measure each side in inches. Then they add up all four sides. This is the perimeter in inches of the court. If necessary, use chalk to write out the equation.

Next give each student two pieces of square (12 by 12) paper with masking tape on the back. Students will lay down their pieces of paper until the entire court is covered. Next, count up the squares. The amount is the area of the court in feet squared. This is why we measure area in square feet.

## Procedures

Tell students that they found the perimeter when they measured the distance around the court. They found the area when they covered the region inside the court. The perimeter of an object is the sum of all of its sides. For instance, to find the perimeter of any square add up all of its sides. Since a square has four equal sides, they can take one side and multiply it by four. An octagon is one side times eight. However, for a polygon with all different sides, each side must be added up.

Area is a little more complicated. For a square or rectangle, multiply the length times the width. Since a triangle is, essentially, half of a square or rectangle, the formula is half of the base times the height.

## Give Me an A! Give Me a P!

Students can become confused when trying to decide whether or not to find perimeter or area. To help remedy this, play a game of “Perimeter or Area.” Give each student a letter P and a letter A. Then pose a series of potential word problems. If students think the problem can be solved using area, they hold up the A. If they think perimeter is the method needed to find the answer, they hold up a P.

*Sarah is making a fence for her garden. The garden is in a rectangle shape and its dimensions are 10 feet by 8 feet. How many feet of fencing does she need to completely enclose her garden?*Students should realize that the word enclose signals around and the word around is solved using perimeter. Add 10+10+8+8 = 36. Another way to solve this problem is 2(10)+ 2(8)=36 ft of fence*Vince needs to redo the carpet in his bedroom. The dimensions of the room are 15 feet by 18 feet. How much carpet does Vince need to cover the entire room?*This problem can be solved using area. Multiply 15 x 18 = 270 sq. feet of carpet The word cover often signifies to use an area formula.*We are getting new grass in our backyard. The backyard is 12 yards by 12 yards. How much grass do we need for the backyard?*This problem can also be solved using area. Multiply 12 x 12 to get 144 sq. yards of grass.

## Perimeter and Area Design

As a fun culmination for the lesson, allow students to design a room, garden or playground. Students will need a ruler, drawing materials and construction paper. Students must give the dimensions of their area and write down how much grass, flooring, fencing or other materials are needed to complete their design. For a backyard, they can design it and use a lot of color. Then, they must write down how many square feet of grass they will need to complete their backyard. Then, they need to write down how many feet (or yards or meters) of fencing needed. Have them share their findings.

In summary, use this lesson plan on perimeter and area to familiarize students with vocabulary and use of the concepts. This is a great way to help kids understand the terms and formulas before doing worksheets or bookwork.

*This article was written from the author’s classroom experience.*