# Area and Perimeter

Australian curriculum number (ACMMG109; ACMNA098; ACMNA291)

Students consolidate their understanding of and skills in calculating the area and the perimeter of rectangles. They observe patterns, reason mathematically and make generalisations.

This sequence is for students who:

• know how to calculate the perimeter and area of rectangles.
• are familiar with the metric units that are used to measure perimeter and area.

### Lesson 1: What Is The Area?

Students explore the relationship between area and perimeter using the context of bumper cars at an amusement park. They design a rectangular floor plan with the largest possible area when given a perimeter of 50 m, and observe that the area of a rectangle increases as the sides get closer in length. Students find that the rectangle with the greatest area for a set perimeter is a square.

### Lesson 2: What Is The Perimeter?

Students explore the possible perimeter of a bumper car ride that has a floor area of 48 m2. They recognise that factors of the area form the dimensions of the possible rectangles. Students graph the results and form the generalisation that the smaller the difference in side lengths, the smaller the perimeter.

### Lesson 3: Designing Bumper Car Rides

Students design three different floor plans for bumper car rides: (i) where the area is numerically greater than its perimeter; (ii) with a perimeter numerically greater than its area; and (iii) with a perimeter numerically equal to its area.

Last updated June 16 2020.