Area of Plane Shapes
Area is the size of a surface!
Learn more about Area, or try the Area Calculator.
Triangle Area = ½ × b × h b = base h = vertical height |
Square Area = a^{2} a = length of side |
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Rectangle Area = w × h w = width h = height |
Parallelogram Area = b × h b = base h = vertical height |
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Trapezoid (US) Trapezium (UK) Area = ½(a+b) × h h = vertical height |
Circle Area = π × r^{2} Circumference = 2 × π × r r = radius |
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Ellipse Area = πab |
Sector Area = ½ × r^{2} × θ r = radius θ = angle in radians |
Note: h is at right angles to b: |
Example: What is the area of this rectangle?
The formula is:
Area = w × h
w = width
h = height
We know w = 5 and h = 3, so:
Area = 5 × 3 = 15
Example: What is the area of this circle?
Radius = r = 3
Area | = π × r^{2} | |
= π × 3^{2} | ||
= π × (3 × 3) | ||
= 3.14159... × 9 | ||
= 28.27 (to 2 decimal places) |
Example: What is the area of this triangle?
Height = h = 12
Base = b = 20
Area = ½ × b × h = ½ × 20 × 12 = 120
A harder example:
Example: Sam cuts grass at $0.10 per square meter
How much does Sam earn cutting this area:
Let's break the area into two parts:
Part A is a square:
Area of A = a^{2} = 20m × 20m = 400m^{2}
Part B is a triangle. Viewed sideways it has a base of 20m and a height of 14m.
Area of B = ½b × h = ½ × 20m × 14m = 140m^{2}
So the total area is:
Area = Area of A + Area of B = 400m^{2} + 140m^{2} = 540m^{2}
Sam earns $0.10 per square meter
Sam earns = $0.10 × 540m^{2} = $54