Area Of Plane Shapes - Math Is Fun

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Math is Fun Area of Plane Shapes

Area is the size of a surface! Learn more about Area, or try the Area Calculator.

triangle base height Triangle Area = ½ × b × h b = base h = vertical height square Square Area = a2 a = length of side rectangle Rectangle Area = w × h w = width h = height parallelogram Parallelogram Area = b × h b = base h = vertical height trapezoid Trapezoid (US) Trapezium (UK) Area = ½(a+b) × h h = vertical height circle Circle Area = π × r2 r = radius ellipse Ellipse Area = πab sector Sector Area = ½ × r2 × θ r = radius θ = angle in radians altitude Note: h is at right angles to b

Example: What is the area of this rectangle?

Area 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?

circle radius 3

Radius = r = 3

Area = π × r2
= π × 32
= π × (3 × 3)
= 3.14159... × 9
= 28.27 (to 2 decimal places)

Example: What is the area of this triangle?

Triangle base=20, height=12

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:

area grass

Let's break the area into two parts:

area grass in parts

Part A is a square:

Area of A = a2 = 20m × 20m = 400m2

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 = 140m2

So the total area is:

Area = Area of A + Area of B = 400m2 + 140m2 = 540m2

Sam earns $0.10 per square meter

Sam earns = $0.10 × 540m2 = $54 1754, 1755, 1756, 1757, 1758, 1759, 1760, 1761, 3250, 3251 Area Calculation Tool Area Area of Irregular Polygons Geometry Index Copyright © 2024 Rod Pierce

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