Irregular shapes: split them up or count the squares
Find the area of an L-shaped room, a T-shaped courtyard, a field with a slanted side and a pond with a curved edge, by splitting them into rectangles and triangles or by counting squares on a 1 m grid.
Core concept
In short: Find the area of odd shapes by cutting them into simple pieces or counting squares.
Split an irregular shape into rectangles and triangles and add their areas; for a curved shape, count the squares at least half inside
Topic: Area and perimeter
Many real shapes are not simple rectangles: an L-shaped room, a T-shaped school courtyard, a field with one slanting side, or a village pond with a curved edge. To find the area: How much flat space a shape covers, measured in square units like cm². All key words of a shape with straight sides, split it into rectangles and triangles, find the area of each, and add them up. For a shape with a curved edge, draw it on a grid of 1 m squares and count: every whole square inside, and every square that is at least half inside, counts as 1 m². The perimeter: The total distance around the edge of a shape. All key words is the distance all the way round the edge.
What you will learn
- Find the area of an irregular shape by splitting it into rectangles and triangles.
- Estimate the area of a curved shape by counting squares.
- Find the perimeter of an irregular shape by adding the lengths round its edge.
Before you start
- Find the area of a rectangle, and of a triangle as ½ × base × height.
Materials
- Squared paper (1 square = 1 m²) and a pencil
Equipment
- A measuring tape and a string, for measuring a real edge
Procedure
- Split the L-shaped room into two rectangles and add their areas.
- Do the same for the T-shaped courtyard.
- Split the field into a rectangle and a triangle.
- Count the squares inside the pond to estimate its area.
How this simulation is simplified
- Each square of the grid is 1 m by 1 m, so it is 1 m².
- When counting, a square counts if it is at least half inside the shape; smaller pieces are left out.
- The pond's perimeter is worked out for its oval shape and rounded to one decimal place.