Area Arena
Master every area formula in the arena: rectangles, triangles, parallelograms and trapezia, circles in terms of π, and composite shapes you split into pieces you already know.
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Area Arena 🏟️
**Area** is the space *inside* a shape (measured in square units); **perimeter** is the distance *around* it. Do not mix them up — a classic dropped mark. Learn a handful of area formulas and one splitting trick for awkward shapes, and you can measure anything in the arena.
Rectangles and triangles ▭
Two to start: • **Rectangle** area = **length × width**. • **Triangle** area = **½ × base × height** (the height is the *perpendicular* height, not a slanted side). A rectangle 8 by 5 has area 8 × 5 = 40. A triangle with base 6 and height 4 has area ½ × 6 × 4 = 12.
Area of a rectangle
An interactive activity.
Area of a triangle
An interactive activity.
Parallelograms and trapezia 🔷
Two more: • **Parallelogram** area = **base × height** (perpendicular height, like a squashed rectangle). • **Trapezium** area = **½ × (a + b) × height**, where a and b are the two parallel sides. A trapezium with parallel sides 4 and 6 and height 3 has area ½ × (4 + 6) × 3 = ½ × 10 × 3 = 15.
Area of a trapezium
An interactive activity.
Match each shape to its area formula
- Rectangle
- Triangle
- Parallelogram
- Trapezium
- length × width
- ½ × base × height
- base × height
- ½ × (a + b) × height
Circles ⭕
For a circle with radius **r**: • **Circumference** (the perimeter) = **2πr** (or πd, since the diameter d = 2r). • **Area** = **πr²**. ⚠️ Use the **radius** in πr², not the diameter — halve the diameter first. Answers are often left "in terms of π" (e.g. 9π) so they stay exact.
Area of a circle
An interactive activity.
Circumference
A circle has radius 3 cm. What is its circumference, in terms of π?
- 6π cm
- 9π cm
- 3π cm
- 36π cm
Composite shapes 🧩
An awkward shape is just simpler shapes joined together. **Split it** into rectangles, triangles or parts of circles, work out each area, then **add** them. Sometimes it is easier to take a big rectangle and **subtract** a cut-out. Either way, break it into shapes you already know.
Split the L-shape
An interactive activity.
Order the method
An interactive activity.
The arena rules
The _____ of a shape is the space inside it, while the perimeter is the distance around it. The area of a circle is π × _____. To find the area of a composite shape, split it into shapes you know and _____ the areas.