What is the formula for the area of a circle?

The area of a circle is calculated using the formula A = π × r², where r is the radius of the circle and π (pi) is approximately 3.14159. This formula derives directly from the geometric relationship between a circle's radius and the space it encloses.

How do you calculate the area of a triangle?

The area of a triangle is A = ½ × base × height, where the height is the perpendicular distance from the base to the opposite vertex. This formula works for all triangles, including right, acute, and obtuse triangles, as long as you use the true perpendicular height.

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📐 Math

Area Calculator (2D Shapes)

Calculate the area of any 2D shape: circle, rectangle, triangle, trapezoid, parallelogram, and ellipse.

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Shape

Radius (r)

Length (l)

Width (w)

Base (b)

Height (h)

Parallel Side a

Parallel Side b

Height (h)

Base (b)

Height (h)

Semi-axis a

Semi-axis b

Area Formulas for Every 2D Shape

Why Area Matters

Area quantifies the 2-dimensional space enclosed within a boundary. It is used in architecture (floor plans), agriculture (field measurement), manufacturing (material coating), and mathematics (integration).

Key Formula Reference

Circle: A = π × r²
Rectangle: A = length × width
Triangle: A = ½ × base × height
Trapezoid: A = ½ × (a + b) × height
Parallelogram: A = base × height
Ellipse: A = π × a × b (where a and b are semi-axes)

The Role of π (Pi)

π (≈ 3.14159) appears in the circle and ellipse formulas because it represents the inherent relationship between a circle's diameter and its circumference — a universal mathematical constant woven into the fabric of circular geometry.