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By the end of these notes, you will be able to:
A compound shape (sometimes called a composite shape) is a flat (2D) shape that is made up of two or more simpler shapes joined together. For example, an L-shape is really just two rectangles put together.
A part of a shape is exactly what it sounds like — a portion or fraction of a standard shape. For example, a semicircle is half of a full circle.
The key idea for both is simple: break the shape into pieces you already know how to deal with, work out what you need for each piece, then combine your answers.
You need these formulas as building blocks. Make sure you know them before trying compound problems.
| Shape | Area | Perimeter/Circumference |
|---|---|---|
| Rectangle | length × width | 2(length + width) |
| Triangle | ½ × base × height | sum of all three sides |
| Circle | πr² | 2πr |
| Semicircle | ½πr² | πr + 2r |
| Quarter circle (quadrant) | ¼πr² | ½πr + 2r |
| Trapezium | ½(a + b)h | sum of all four sides |
| Parallelogram | base × height | sum of all four sides |
r = radius of a circle (the distance from the centre to the edge) π (pi) ≈ 3.14159… — a special number used in all circle calculations. Sometimes your answer must be left in terms of π, meaning you write π as a symbol rather than using its decimal value.
The perimeter is the total distance all the way around the outside edge of a shape.
Steps:
⚠️ Watch out: When two shapes are joined together, the edges where they meet are no longer on the outside. Do not include those internal edges in your perimeter.
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