Area Quadrilateral Calculator - Per-Shape And General Area

An area quadrilateral calculator finds the enclosed area of any four-sided shape, from a familiar rectangle to an irregular quadrilateral you can only describe with diagonals and an angle. It accepts the right inputs for each variant, applies the matching formula, and returns the result in the squared form of your chosen unit.

• • Homework and geometry class: Confirm the area of a rectangle, square, parallelogram, rhombus, trapezoid, or kite from your inputs.
• • Floor plans and room sketches: Read the area of a rectangular or trapezoidal space for flooring or carpeting estimates.
• • Landscaping and paving: Estimate the area of a sloped or angled paved section by entering base and height or parallel sides and height.
• • Irregular four-sided plots: Use the general mode when you only know the two diagonals and the angle at which they cross, which is common when surveying an uneven lot.

The strength of an area quadrilateral calculator is that it does not force you to remember six different formulas. The selector tells the tool which inputs matter, so you can focus on the numbers you actually have.

When the four-sided shape is just one slice of a larger layout, the next step is usually a different calculator tuned to the rest of that layout.

When the four-sided shape is one slice of a larger regular polygon, the result also lines up neatly with the apothem and side-length math used by the Polygon Area Calculator.

The calculator picks the formula that matches the quadrilateral type you chose, then reads the relevant inputs and reports the area. Each shape has its own compact rule, and the general mode falls back to the half-diagonal-product formula when only the diagonals and the angle between them are known.

• L, W: Length and width of a rectangle, in the same linear unit.
• s: Side length of a square, used in both area and perimeter.
• b, h: Base and perpendicular height of a parallelogram.
• a, b, h: Two parallel sides and the perpendicular height of a trapezoid.
• d1, d2: The two diagonals of a rhombus, kite, or general quadrilateral.
• theta: The angle at which the two diagonals cross, in degrees.

For each shape, the calculator also reports the perimeter when enough side information is in the form, and the formula line names the rule that was applied. The general mode is a close cousin of Bretschneider's formula, which uses two opposite angles and a semiperimeter for the same shape family.

According to Wolfram MathWorld, the area of an irregular quadrilateral with diagonals d1 and d2 meeting at angle theta is A = 0.5 * d1 * d2 * sin(theta).

According to Wolfram MathWorld, the area of a general quadrilateral with sides a, b, c, d and opposite-angle sum (alpha + gamma) is A = sqrt((s-a)(s-b)(s-c)(s-d) - a*b*c*d*cos^2(0.5*(alpha+gamma))), where s is the semiperimeter.

When you need a side-by-side comparison across several two-dimensional shapes, the Area Calculator runs the same inputs and outputs in a single form for rectangles, triangles, circles, ellipses, and more.

A few terms come up again and again when you compare the formulas. They are short, but they decide which input on the form is the right one to use.

Knowing which of these applies to your shape is what tells the calculator which formula to use. Once that is settled, the actual arithmetic is short.

For an unrelated shape with curved sides, the Circle Calculator gives the matching inputs and area formula for circles, ellipses, and arcs.

Pick the shape that matches your drawing, fill in the inputs that apply, and read the area on the right. The unit selector changes every result at once.

1. 1 Select the quadrilateral type: Use the dropdown. Pick the specific shape if you can; otherwise choose General when only the diagonals and the crossing angle are known.
2. 2 Enter the relevant length inputs: For a rectangle, fill in length and width. For a parallelogram, fill in base and perpendicular height. For a rhombus or kite, fill in the two diagonals. For a general quadrilateral, fill in the two diagonals and the angle between them.
3. 3 Choose the linear unit: Pick the unit you are measuring with. The area will be reported in the matching squared unit, so feet surface as square feet.
4. 4 Read the area and supporting values: The right panel shows the area, the perimeter when available, and the formula that was applied. Confirm the formula line matches the shape you selected.
5. 5 Compare against related shapes when needed: If the result looks too high or too low, switch the type to a different quadrilateral to see how the answer changes.

A paving plan shows a sloped rectangle 6 m long, 4 m wide on the long side, and 3 m wide on the short side. Pick Trapezoid, set the parallel sides to 6 and 4, and the height to 3. The result is 15 square meters.

When the four-sided shape is actually two triangles joined along a diagonal, the Triangle Calculator is the right companion to confirm each triangle before you add the pieces back together.

The tool replaces a stack of separate area formulas with a single form. Once you have the right inputs, the rest of the work happens in one place.

• • One form for six named shapes plus a general mode: Switch between rectangle, square, parallelogram, rhombus, trapezoid, and kite without leaving the page. Unused inputs are simply ignored.
• • Reads the inputs you can actually measure: Diagonals, parallel sides, and the angle at which diagonals meet are all valid starting points, so the matching formula is the one the calculator applies.
• • Live updates as you type: Every change to the type, the side values, the diagonals, or the unit updates the area, the perimeter, and the active formula immediately.
• • Honest about which inputs it uses: The result panel names the formula applied, so you can confirm whether you are looking at the rectangle, trapezoid, or general rule before you trust the value.
• • Pairs with related shape work: The same area units and input style are used here, so swapping between a four-sided shape and a triangle or a circle is a one-click comparison.

When the result is part of a bigger layout, the follow-up question is often the reverse problem: given a known area and one more measurement, recover the missing side. That calculation has its own dedicated form for rectangles.

When the result is part of a bigger layout, the Length Width Area Rectangle Calculator covers rectangles where you only know area and perimeter and want to recover the length and width.

Most mistakes with this kind of calculation come from the wrong input or the wrong shape type, not from the formula itself. A short checklist before you read the area keeps the result honest.

• • Concave quadrilaterals, sometimes called dart or arrowhead shapes, are not handled by these formulas because the diagonals sit partly outside the figure. Use a triangle-based decomposition for those shapes.
• • The general mode is an approximation when the only data you have is the two diagonals and the crossing angle; a small error in the angle produces a noticeable error in the area because the formula is multiplied by sin(theta).
• • Mixing side inputs and diagonal inputs across different unit families is the fastest way to land on a result that looks plausible but is wrong.

For the per-shape rules, the same identities that drive each named mode here are well documented on the per-shape reference pages. The links at the end of this section point to the broader two-dimensional area family and to the unit-conversion case so the rest of a layout stays consistent with the four-sided piece.

According to Math Open Reference, a rectangle's area equals length times width, a parallelogram's area equals base times height, a rhombus's area equals half the product of its diagonals, and a trapezoid's area equals half the height times the sum of the parallel sides.

If the result needs a different area unit, the Area Converter handles square-meter, square-foot, acre, and hectare conversions so the four-sided piece stays consistent with the rest of the layout.