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Math Foundations

Determine the smallest or largest possible perimeter given a fixed area, and determine the smallest or largest possible area given a fixed perimeter.

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After completing this tutorial, you will be able to complete the following:

- Distinguish between perimeter and area.
- Determine the largest or smallest perimeter, given the area.
- Determine the largest or smallest area, given the perimeter.

Area

Area is the measurement of interior space of a two-dimensional shape, or the surface of three-dimensional figure; it is the amount of surface a shape covers. Area is measured in square units. The area of the rectangle can be calculated using the following formula: A = l × w, where l represents the length and w represents the width.

For the shape above, the length equals 4 units and the width equals 3 units. A = l × w

A = 4 × 3 = 12 square units

Perimeter

Perimeter is the length of the boundary of the shape. It can be calculated adding the measurements of each side. For a rectangle, it can be calculated using the following formula: P = l + w + l + w, or P = 2l + 2w.

For the shape above, the length equals 4 units and the width equals 3 units.P = 4 + 3 + 4 + 3 P = (2 × 4) + (2 × 3) = 14 units

Area and perimeter of irregular shapes

If irregular shapes are drawn on grid paper, as in the Activity Object, you can use the grid to help you calculate the area and perimeter.

- For area, simply count all the unit squares that make up the shape:There are 12 unit squares that make up this shape, so the area equals 12 square units.
- For perimeter, count the sides of each unite square that makes up the shape: There are 24 units that make up the perimeter of shape. Therefore, the perimeter equals 24 units.

Approximate Time | 20 Minutes |

Pre-requisite Concepts | Students should know the definitions of area and perimeter. |

Course | Math Foundations |

Type of Tutorial | Concept Development |

Key Vocabulary | area, perimeter, shape |