How this calculator works
A right trapezoid splits into a rectangle and a right triangle. The triangle has horizontal leg equal to the difference between the bases, vertical leg equal to the height and hypotenuse equal to the slanted side. This determines the two non-right angles. The area table adds the rectangle and triangle contributions. Reverse modes recover the height from the supplied area, slanted side, perimeter or acute angle.
Formula
g = |a - b|; d = hypot(g,h); A = (a+b)h/2; P = a+b+h+d; acute θ = atan2(h,g). From P, let q=P-a-b: h=(q²-g²)/(2q).
Worked example
Bases 7 m and 3 m with height 3 m give gap 4 m and slanted side 5 m. The rectangle contributes 9 m² and the right triangle 6 m², for 15 m² total. Perimeter is 7 + 3 + 3 + 5 = 18 m.
Advertisement
Frequently asked questions
Can the slanted side be used as the height?
Only when the bases are equal and the shape is a rectangle. Otherwise the slanted side is longer than the perpendicular height.
Which base must be longer?
Either one. The tool uses the absolute difference, so swapping the bases keeps the reported dimensions and angle magnitudes unchanged.
What happens with equal bases?
Height, area, slant and perimeter modes accept the resulting rectangle. All four angles are 90°. Angle mode cannot recover a height from that information alone.