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Calculate the area of common 2D shapes: circle, rectangle, triangle, trapezoid, parallelogram, ellipse, and regular polygon.
Area Formulas:
Circle: A = π × r²
Rectangle: A = l × w
Triangle: A = (1/2) × b × h
Trapezoid: A = (1/2) × (a + b) × h
Parallelogram: A = b × h
Ellipse: A = π × a × b
Regular Polygon: A = (n × s²) / (4 × tan(π/n))
Area measures the amount of 2D space enclosed by a shape. It is expressed in square units (cm², m², in², ft², etc.).
A regular polygon has n equal sides of length s. Its area is A = (n × s²) / (4 × tan(π/n)). For a regular hexagon with side 5: A = (6 × 25) / (4 × tan(30°)) ≈ 64.95 square units.
A rectangle is a parallelogram with all right angles. Both use A = base × height, but in a parallelogram the height is the perpendicular distance between the two parallel bases, not the slant side length.
If you know the diameter d, the radius r = d/2. Then apply A = π × r². For a circle with diameter 10: r = 5, A = π × 25 ≈ 78.54 square units.
An ellipse is a stretched circle defined by two semi-axes: a (longer, semi-major) and b (shorter, semi-minor). Its area is A = π × a × b. When a = b = r, this reduces to the circle formula A = π × r².