Right Trapezoid Calculator
Enter the two parallel bases and perpendicular height to calculate area, slant side, perimeter, median, and all four interior angles.
Dimensions
One parallel side; it may be longer or shorter than base b.
The other parallel side; equal bases produce a rectangle.
The perpendicular leg and distance between the bases.
Changing units converts all three entered dimensions.
Calculated properties
Area (A)
47.5 cm²
Slant side (d)
7.0711 cm
Perimeter (P)
31.0711 cm
Median
9.5 cm
Acute angle
45°
Obtuse angle
135°
Right angles
2
Area 47.5 square centimeters. Perimeter 31.0711 centimeters.
Property details
| Property | Formula | Current value |
|---|---|---|
| Area (A) | (a + b) × c ÷ 2 | 47.5 cm² |
| Slant side (d) | √((a – b)² + c²) | 7.0711 cm |
| Perimeter (P) | a + b + c + d | 31.0711 cm |
| Median | (a + b) ÷ 2 | 9.5 cm |
| Acute angle | atan(c ÷ |a – b|) | 45° |
| Obtuse angle | 180° – acute angle | 135° |
All values use the same canonical model as the live result cards and Excel workbook. Displayed decimals are rounded; the workbook stores full finite numeric precision.
How to use the right trapezoid calculator
What this calculator does
This calculator finds the main properties of a right trapezoid from its two parallel bases and its perpendicular side. A right trapezoid has two right angles, so the perpendicular side is also the height. From those three dimensions, the calculator determines the area, slant side, perimeter, median, acute angle, and obtuse angle. It is a geometry calculator, not a drawing or surveying tool: it assumes straight sides, parallel bases, positive dimensions, and measurements expressed in one consistent unit.
When to use it
Use it to check a homework solution, estimate the area and boundary length of a trapezoidal panel or plot, determine the unknown sloping edge for fabrication, or compare how changing one base affects the angles and perimeter. It is also useful when a rectangular section transitions to a narrower width and the cross-section can be modeled as a right trapezoid.
How to calculate
- The calculator opens with a complete demonstration: Base a = 12 cm, Base b = 7 cm, and Side c (height) = 5 cm. The results and a validated example Excel workbook are available immediately.
- Replace Base a, Base b, and Side c (height) with positive decimal measurements. A dot is the decimal separator; standard comma grouping such as 1,250.5 is accepted.
- Select the Length unit. Changing it converts the three current dimensions and updates every length and area result. Area is displayed in the squared form of the selected unit.
- Read Area (A) as the primary result, then review Slant side (d), Perimeter (P), Median, Acute angle, Obtuse angle, and Right angles. The Property details table shows the exact formula associated with each value.
- Select Download Excel to export the current inputs and full-precision results as a real XLSX workbook. Select Reset to clear the demonstration and all calculated content. Reset may disable Download Excel until all three required dimensions are entered again.
Input guide
Base a and Base b are required positive lengths for the parallel sides. Either may be the longer base. Values such as 12 or 7.5 are valid; zero, negative values, scientific notation, and decimal-comma notation are rejected. Increasing either base increases area, median, and usually perimeter. A common mistake is to enter a nonparallel side as a base.
Side c (height) is the required positive perpendicular leg. In a right trapezoid, this side is exactly the distance between the two parallel bases. A value such as 5 cm is valid. Increasing it increases area, slant side, and perimeter, while also changing the non-right angles. Do not enter the slant side here.
Length unit is required and applies to all three dimensions. The available choices are millimeters, centimeters, meters, inches, and feet. A unit change converts entered values rather than relabeling them, so 12 cm becomes 0.12 m. Mixing units between fields is a common interpretation error; convert everything to one unit first or use the selector.
Output guide
Area (A) is the exact planar area identity before display rounding, shown in square units. Slant side (d) is the nonperpendicular leg, found with the Pythagorean theorem. Perimeter (P) is the total boundary length. Median is the segment parallel to the bases halfway between them and equals their average. Acute angle and Obtuse angle are the two non-right interior angles; they add to 180°. Right angles is normally 2, but becomes 4 when the bases are equal and the shape is a rectangle. These are deterministic geometric results, not statistical estimates.
Worked example
With Base a = 12 cm, Base b = 7 cm, and height c = 5 cm, the area is (12 + 7) × 5 ÷ 2 = 47.5 cm². The horizontal offset is |12 – 7| = 5 cm, so the slant side is √(5² + 5²) = √50 = 7.0711 cm when displayed to four decimals. The perimeter is 12 + 7 + 5 + 7.0711 = 31.0711 cm, and the median is (12 + 7) ÷ 2 = 9.5 cm. Because the offset and height are equal, the acute angle is 45° and the obtuse angle is 135°.
Learn more
The OpenStax explanation of trapezoid area derives A = ½h(a + b). The slant calculation follows the Pythagorean theorem for right triangles, and the angle calculation uses the tangent relationship described in OpenStax right-triangle trigonometry.
Formulas and interpretation
d = √((a – b)² + c²)
P = a + b + c + d
m = (a + b) / 2
The two bases contribute through their sum in the area formula and through their difference in the slant and angle formulas. That distinction matters: shifting both bases upward by the same amount increases area and perimeter but leaves the slant-side offset unchanged. When a = b, the offset is zero and the right trapezoid becomes a rectangle with four 90° angles.