Area by cutting and rearranging – parallelogram, triangle, trapezium, rhombus, composite shapes
MathematicsPlane GeometryAges 11–12
Loading…
Sign in to playDrag the base, height and offset of a parallelogram, triangle or trapezium and watch it being cut and rearranged into a rectangle or parallelogram (a triangle is half a parallelogram, two trapeziums make a parallelogram) to derive A = bh, A = ½bh and A = ½(a + b)h. A rhombus or kite fills half of the d₁ × d₂ rectangle, so A = ½d₁d₂. On a square grid, split L, T, U and stepped shapes into rectangles for area and perimeter, and estimate the area of a curved shape by counting squares; convert between cm², mm² and m².
Lesson: Area of rectangles, parallelograms, triangles, trapeziums (trapezoids) and rhombuses; area and perimeter of composite shapes; estimating area by counting squares
What it shows
Area is conserved when a shape is cut into pieces that are only slid or turned. Cutting a parallelogram along its perpendicular height and sliding the triangle across makes a rectangle, so A = bh. Two copies of a triangle form a parallelogram, so a triangle is half of it: A = ½bh. Two copies of a trapezium form a parallelogram with base a + b, so A = ½(a + b)h. A rhombus or kite with perpendicular diagonals fills exactly half of the d₁ × d₂ rectangle. Composite shapes are split into rectangles, and the area of a curved shape can be estimated by counting squares.
How to use
Choose a tab. Drag the round handles or use Base b, Height h, Top side a and Offset, then press Cut and rearrange or drag Progress. In Rhombus and kite set Diagonal d₁ and Diagonal d₂. In Square grid pick a Shape and a Split method, tick Number the squares, and drag the handles; for the curved shape press New shape. Unit switches between cm and m.
Parameters you can change
- Mode Parallelogram → rectangle, Triangle as half a parallelogram, Two trapeziums make a parallelogram, Rhombus, kite and diagonals, Square grid: composite shapes and estimation
- Base b (width on the grid) 2–10
- Height h 1–7
- Top side a of the trapezium 1–8
- Offset of the top side (apex) -3–6
- Diagonal d₁ 2–10
- Diagonal d₂ 2–7
- Shape with perpendicular diagonals Rhombus, Kite
- Shape on the grid L-shape, T-shape, U-shape, Stepped shape, Curved shape (estimate)
- Unit of length Centimetre (cm), Metre (m)
Questions to explore
- Why does a parallelogram have the same area as a rectangle with the same base and height?
- If a triangle's apex moves sideways parallel to the base, what happens to its area?
- Which way of splitting an L-shape into rectangles needs the fewest calculations?
