2D Shapes

A = a² — A square has four equal sides and four right angles. Its diagonal splits it into two isosceles right triangles.

A = l × w — A rectangle has opposite sides equal and four right angles. Its diagonal follows from the Pythagorean theorem.

A = ½ b h — The area of any triangle is half its base times its perpendicular height. Its perimeter is the sum of the three sides.

A = (√3 ⁄ 4) a² — All three sides are equal and every angle is 60°. Area, height and perimeter depend only on the side length.

A = πr² — Every point on a circle is the same distance r from the centre. π (pi) ≈ 3.14159 links the radius to the circumference and area.

A = πab — An ellipse is a stretched circle with a semi-major axis a and a semi-minor axis b. The perimeter has no simple exact formula, so Ramanujan’s approximation is used.

A = b × h — A parallelogram has two pairs of parallel sides. Its area is base times perpendicular height, not base times slanted side.

A = ½ (a + b) h — A trapezoid (trapezium) has one pair of parallel sides. Its area is the average of the parallel sides times the height.

A = ½ p q — A rhombus has four equal sides. Its diagonals cross at right angles, so its area is half the product of the diagonals.

A = (θ ⁄ 360) πr² — A sector is a “pizza slice” of a circle bounded by two radii and an arc. Its share of the circle equals θ ⁄ 360°.

A = n s² ⁄ (4 tan(π⁄n)) — A regular polygon has n equal sides and n equal angles: pentagons, hexagons, octagons and more.