About this calculator
Area is needed for flooring, painting, plates, land plots and cross-sections. Choose the shape and enter its dimensions in any unit. For a triangle you only need the three side lengths — no height is required.
Formula
Rectangle
A = L × W P = 2(L + W)
Triangle (3 sides)
s = (a + b + c) ÷ 2 A = √(s(s − a)(s − b)(s − c))
Heron’s formula. Perimeter P = a + b + c.
Trapezoid
A = (a + b) ÷ 2 × h
a, b = the two parallel sides, h = perpendicular distance between them.
Ellipse
A = πab
P ≈ π[3(a + b) − √((3a + b)(a + 3b))]
a, b = semi-axes. The perimeter of an ellipse has no simple exact formula; this is Ramanujan’s approximation.
Worked example
- Rectangle 4 m × 3 m: area 12 m², perimeter 14 m.
- Triangle with sides 3, 4 and 5 m: s = 6, area = √(6 × 3 × 2 × 1) = 6 m².
- Trapezoid with parallel sides 6 m and 4 m, height 5 m: area = 5 × 5 = 25 m².
- Ellipse with semi-axes 5 m and 3 m: area = π × 15 = 47.12 m², perimeter ≈ 25.53 m.
Assumptions and limitations
- Flat (plane) shapes with straight sides, except the ellipse.
- For land and plots, real boundaries are rarely perfect shapes; divide irregular areas into triangles and add them up.
References
- Plane geometry; Heron’s formula; Ramanujan (1914) approximation for the ellipse perimeter.