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The area of an isosceles (or any) trapezoid is equal to the average of the lengths of the base and top (the parallel sides) times the height. In the adjacent diagram, if we write AD = a , and BC = b , and the height h is the length of a line segment between AD and BC that is perpendicular to them, then the area K is
This yields as a special case the well-known formula for the area of a triangle, by considering a triangle as a degenerate trapezoid in which one of the parallel sides has shrunk to a point. The 7th-century Indian mathematician Bhāskara I derived the following formula for the area of a trapezoid with consecutive sides a, c, b, d:
Heron's formula is a special case of Brahmagupta's formula for the area of a cyclic quadrilateral. Heron's formula and Brahmagupta's formula are both special cases of Bretschneider's formula for the area of a quadrilateral. Heron's formula can be obtained from Brahmagupta's formula or Bretschneider's formula by setting one of the sides of the ...
Isosceles trapezium (UK) or isosceles trapezoid (US): one pair of opposite sides are parallel and the base angles are equal in measure. Alternative definitions are a quadrilateral with an axis of symmetry bisecting one pair of opposite sides, or a trapezoid with diagonals of equal length.
The area, perimeter, and base can also be related to each other by the equation [23] + = If the base and perimeter are fixed, then this formula determines the area of the resulting isosceles triangle, which is the maximum possible among all triangles with the same base and perimeter. [24]
The British flag theorem can be generalized into a statement about (convex) isosceles trapezoids.More precisely for a trapezoid with parallel sides and and interior point the following equation holds:
The yellow dots show the position uncertainty of asteroid 2024 YR4 when it encounters Earth in 2032, based on observations up to January 31, 2025.
Isosceles-triangular area: Right-triangular area Circular area: Quarter-circular area [2] Semicircular area [3] Circular sector Circular segment () ...