What is a 2D Shape Area Calculator?
This calculator computes the area of triangles, quadrilaterals, trapezoids, rhombuses, and other 2D shapes.
How it's calculated
Triangle = base × height ÷ 2
Trapezoid = (top + bottom) × height ÷ 2
Rhombus = diagonal × diagonal ÷ 2
Step-by-step example
Area of a trapezoid with top 4cm, bottom 8cm, height 5cm
- Step 1 Apply the formula: area = (top+bottom)×height÷2
- Step 2 Calculate: (4+8)×5÷2 = 60÷2
- Step 3 Result: 30 cm²
Interpretation: This formula comes from joining two copies of the trapezoid, flipped, into a parallelogram.
You don't have to memorize these formulas
Every one of these formulas traces back to a single rectangle. A triangle, flipped and joined to a copy of itself, forms a parallelogram (hence ÷2). A trapezoid, similarly flipped and joined, forms a parallelogram with base equal to top+bottom (hence ÷2 again). It's all the same story: cut it, rearrange it, turn it into a rectangle. Once you see that pattern, you can reconstruct any of these formulas on the spot if you forget it.
Good to know
- Heron's formula computes a triangle's area from its three side lengths alone, with no height needed — handy when you can only measure with a tape.
- Among shapes with the same perimeter, a circle has the largest area — the same reason soap bubbles form spheres, minimizing surface area for a given volume.
- An irregular plot of land is typically measured by splitting it into triangles and summing their areas — any polygon can be decomposed this way.
- 1 hectare = 10,000 m², roughly the size of a large sports field, and a common reference for measuring land area.
- The founding legend of Carthage tells of Queen Dido, who was granted 'as much land as an ox hide could cover' and cleverly cut the hide into an extremely thin strip to enclose a much larger area — an early intuition about the isoperimetric problem.
Frequently asked questions
Q. How do I find a triangle's area without knowing the height?
Use Heron's formula with all three sides, or use ½×a×b×sinC if you know two sides and the included angle.
Q. Where exactly is trapezoid height measured?
The perpendicular distance between the two parallel sides, not the length of a slanted side.
Q. How do I find the area of an irregular plot?
Split it into triangles, calculate each area separately, and sum them.