Calculate the area of rectangles, triangles, circles, trapezoids, ellipses and sectors.
Area measures the two-dimensional space enclosed by a shape. Rectangle area is length × width. A triangle is half the base times the height. A circle is πr². A trapezoid uses the average of the two parallel sides times the height. An ellipse generalises the circle formula using its two semi-axes. A sector is a fraction of a full circle's area determined by the central angle. A parallelogram is base times perpendicular height.
Rectangle
A = length × width
Triangle
A = ½ × base × height
Circle
A = π × r²
Trapezoid
A = ½ × (a + b) × height
Ellipse
A = π × semi-major × semi-minor
Sector
A = (θ/360°) × π × r²
Parallelogram
A = base × height
Area is the space inside a shape, measured in square units (cm², m², ft²). Perimeter is the total length of the boundary, measured in linear units (cm, m, ft).
A triangle is exactly half of a parallelogram (or rectangle) with the same base and height. You can see this by duplicating any triangle and fitting the copy alongside the original to form a parallelogram.
Divide it into simpler sub-shapes whose areas you can calculate, then add them up. Alternatively, use the Shoelace formula if you know all the vertex coordinates.