Right Trapezoid Area Calculator

How to use this right trapezoid area calculator

What this calculator does

This calculator finds the area of a right trapezoid and reports related dimensions that are useful for checking a drawing, worksheet, fabrication layout, or land-measurement sketch. A right trapezoid has one pair of parallel sides and a perpendicular leg, so that leg is also the height. The core result is the exact geometric identity A = (a + b) × h ÷ 2. The tool also derives the midsegment, slant side, perimeter, acute angle, and obtuse angle. It does not determine whether a real-world object is level, square, or accurately measured; those depend on the quality of the source measurements.

When to use it

Use the calculator when you need the surface area of a right-trapezoid panel, the plan area of a trapezoidal section, a geometry homework check, or a quick dimensional review before estimating material. It is also useful when the perpendicular height is not written directly but you know either the slant side or the acute angle formed by the sloped leg.

How to calculate

1. The calculator opens with a complete demonstration: Base a = 10 cm, Base b = 6 cm, and Height h = 4 cm. Its area and a validated example workbook are available immediately.
2. Replace Base a and Base b with the two positive parallel-side lengths from your figure.
3. Choose Height source. Select direct height when h is known, slant side when d is known, or acute angle when δ is known.
4. Enter the active measurement and choose the Length unit. A unit change converts current length values, including hidden method fields, so the geometry remains the same.
5. Read Area first, then use the secondary results and Geometry details table to verify the shape. Select Download Excel to export the current typed model as a real .xlsx workbook.
6. Select Reset to clear the demonstration and all calculated content. Reset may disable Download Excel until you enter another complete valid set.

Input guide

Base a and Base b are required positive decimal lengths in the selected unit. Values such as 10, 6.5, or 1,250.25 are accepted under the documented dot-decimal convention. A decimal comma such as 1,5 is rejected rather than silently read as 15. Either base may be longer; swapping them leaves the area unchanged. Increasing either base increases area, midsegment, and perimeter.

Height source is required. With Enter height directly, Height h is a required positive length; 4 cm is the startup example. With Derive from slant side, Slant side d is required and must be longer than the horizontal difference |a – b| unless the bases are equal. The calculator then applies the Pythagorean theorem. With Derive from acute angle, Acute angle δ is required, must be between 0° and 90°, and requires unequal bases; 45° is a common example. The height is |a – b| × tan(δ). Do not enter the obtuse interior angle in this field.

Length unit controls every linear result and the squared area unit. Available choices are millimeters, centimeters, meters, inches, and feet. Mixing measurements from different units without converting them first is a common source of error. The underlying area formula and the definition of trapezoid height are explained in the Khan Academy lesson on trapezoid area.

Output guide

Area is the exact two-dimensional measure in squared selected units. A larger average base or greater height produces a larger area; zero area is not accepted because this calculator models a nondegenerate trapezoid. Height is the perpendicular base separation. Midsegment is (a + b) ÷ 2 and equals area divided by height. Slant side is the nonperpendicular leg. Perimeter is the sum of both bases, height, and slant side. Acute angle and Obtuse angle are the two non-right interior angles and always sum to 180°. The summary pills repeat the active method, area, and perimeter from the same canonical model.

Worked example

For Base a = 10 cm, Base b = 6 cm, and Height h = 4 cm, the average base is (10 + 6) ÷ 2 = 8 cm. Multiplying by the height gives A = 8 × 4 = 32 cm². The base difference is 4 cm, so the slant side is √(4² + 4²) = 5.6569 cm. The perimeter is 10 + 6 + 4 + 5.6569 = 25.6569 cm, and the sloped leg forms a 45° acute angle.