Estimating answers (age 9+)
Apply the area formula (l × w) and perimeter formula (2l + 2w) for rectangles including squares in real-world and mathematical problems; calculate and compare areas using standard units (cm², m²) and estimate areas of irregular shapes
What a learner can do afterwards
- Find the width of a room given area = 48 m² and length = 8 m
- Calculate the area of a square with side 7.5 cm
- Estimate the area of an irregular pond drawn on a cm² grid
The lesson
The area of a rectangle tells you how much flat space it covers. You find it by multiplying the length by the width: area = length × width. Measure in centimetres and you get square centimetres (cm²). Measure in metres and you get square metres (m²).
A square tile has sides of 7.5 cm. Since a square is just a rectangle with equal sides, area = 7.5 × 7.5 = 56.25 cm². You can also work backwards: a room has an area of 48 m² and a length of 8 m, so its width is 48 ÷ 8 = 6 m.
You already know how to find a perimeter by adding up every side. For a rectangle, there's a shortcut, because opposite sides match: perimeter = 2 × length + 2 × width.
Not every shape is a tidy rectangle. To estimate the area of something like a pond, draw it on a grid of squares. Count the whole squares inside it, then guess how the part-covered squares add up, and combine the two counts.
Area = length × width, perimeter of a rectangle = 2 × length + 2 × width, and for odd shapes, count grid squares to estimate.
Watch it
Where it sits
Where this leads
8 questions wait behind this lesson, each with its answer explained. Every answer feeds the sky: stars light as they are learned, and dim when it is time to come back.