Geometry
Area Calculator — 6 Common Shapes
Pick a shape, enter its dimensions, and get the area instantly — plus perimeter or circumference where it can be calculated from the inputs you've provided.
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Disclaimer: This tool performs standard mathematical calculations for educational and reference purposes. Always double-check results independently for graded coursework, exams, or safety-critical applications.
Finding the Area of Common Shapes
Area measures how much flat surface a shape covers, expressed in square units (like square meters or square feet). Each shape has its own formula, but most of them come down to multiplying two related dimensions together.
The Formulas
- Square: A = s² (perimeter = 4s)
- Rectangle: A = length × width (perimeter = 2(length + width))
- Triangle: A = ½ × base × height
- Circle: A = πr² (circumference = 2πr)
- Trapezoid: A = ½ × (base1 + base2) × height
- Parallelogram: A = base × height
Worked Example
A rectangular garden plot measures 8 meters long by 5 meters wide.
- Step 1: A = length × width = 8 × 5 = 40 m²
- Step 2: Perimeter = 2(8 + 5) = 2 × 13 = 26 m
Frequently Asked Questions
Any triangle can be thought of as exactly half of a parallelogram sharing the same base and height. If you duplicate a triangle and rotate the copy 180°, the two pieces fit together to form a parallelogram with area base × height, so a single triangle is naturally half of that.
Perimeter is the sum of all side lengths, but the area formulas for triangles, trapezoids, and parallelograms only require base and height measurements — not every side. Since the remaining side lengths aren't collected as inputs, an accurate perimeter can't be computed for those three shapes here.
A parallelogram has two pairs of parallel sides that are equal in length, like a slanted rectangle. A trapezoid has only one pair of parallel sides, called the two bases, which are typically different lengths — that's why its area formula averages the two bases before multiplying by height.
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