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Area Calculator

Area formulas for common shapes include length × width for rectangles, (base × height)/2 for triangles, and pi × r² for circles. Select a shape and enter dimensions to calculate area instantly.

Quick Answer

A rectangle with length 10 and width 5 has an area of 50 square units. A circle with radius 7 has an area of approximately 153.94 square units.

Common Examples

Input Result
Rectangle: 10 × 5 50 sq units
Triangle: base 8, height 6 24 sq units
Circle: radius 7 153.94 sq units
Trapezoid: bases 6 and 10, height 4 32 sq units

How It Works

Rectangle: A = length x width

Multiply the length by the width. For a rectangle with length 10 and width 5, the area is 50 square units.

Triangle: A = (base x height) / 2

Multiply the base by the height and divide by 2. This formula uses the base and perpendicular height, not the side lengths.

Circle: A = π x r²

Multiply π (approximately 3.14159) by the radius squared. For a circle with radius 7, the area is approximately 153.94 square units.

Trapezoid: A = ((a + b) / 2) x h

Add the two parallel bases, divide by 2, then multiply by the perpendicular height between them.

Ellipse: A = π x a x b

Multiply π by the semi-major axis (a) and the semi-minor axis (b). When a = b, this reduces to the circle formula.

Worked Example

For a circle with radius 7: Area = pi × 7² = pi × 49 ≈ 153.94 square units. For a triangle with base 8 and height 6: Area = (8 × 6) / 2 = 24 square units. For a trapezoid with parallel sides 6 and 10, and height 4: Area = ((6 + 10) / 2) × 4 = 8 × 4 = 32 square units.

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Frequently Asked Questions

What units does the area calculator use?
The calculator works with any consistent unit. If you enter dimensions in centimeters, the result is in square centimeters. If you enter dimensions in feet, the result is in square feet. The output label shows 'square units' as a generic placeholder.
What is the difference between area and perimeter?
Area measures the surface enclosed by a shape, expressed in square units. Perimeter measures the total distance around the outside of a shape, expressed in linear units. For example, a 4x3 rectangle has an area of 12 square units and a perimeter of 14 units.
How do I calculate the area of an irregular shape?
For irregular shapes, you can divide the shape into simpler shapes (rectangles, triangles, etc.), calculate each area separately, and add them together. This approach works well for L-shaped rooms, complex floor plans, and similar real-world problems.
What is the difference between the semi-major and semi-minor axis of an ellipse?
The semi-major axis (a) is the longer radius of the ellipse, measured from the center to the farthest edge. The semi-minor axis (b) is the shorter radius, measured from the center to the nearest edge. When both are equal, the ellipse is a circle.