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The Trapezium is a flat four sided plate with a parallel top edge and bottom edge of different lengths, and two slanted sides of equal length. It is symmetrical about its vertical centre line (an isosceles trapezium, called a trapezoid in North America). It is sized by its Top Width, Bottom Width and Height. Fillet R rounds all four corners with one radius. Use it for tapered plates, end plates, gussets and spacers. For a trapezium whose top edge is not centred over the bottom edge, use the Asymmetric Trapezium.

It appears in the shapes library under Basic Shapes and Other Shapes.

Insert point and orientation

The insert point is the bottom left corner of the sharp outline, at X 0, Y 0. The bottom edge runs to the right along X for Bottom Width. The top edge is Height above it and is centred over the bottom edge, so each end of the top edge is set in by (Bottom Width − Top Width) / 2 from the end of the bottom edge. With Fillet R above 0 the corners are rounded inwards from these sharp corners, so the insert point is then not on the outline.

With the default sizes the sharp corners are at (0, 0), (25, 50), (100, 50) and (125, 0) mm. The bottom corners are about 63.4° and the top corners about 116.6°.

Top Width can be larger than Bottom Width. The shape then widens upwards (a dovetail). The insert point is still the bottom left corner, and the top edge overhangs it to the left by (Top Width − Bottom Width) / 2. With Top Width equal to Bottom Width the shape is a rectangle. With Top Width 0 it is a triangle.

Properties

Lengths are in the current units, mm or inches. The defaults shown are the metric values. When the program is set to inches the defaults are 5 in (Bottom Width), 3 in (Top Width) and 2 in (Height), the same proportions scaled to four inches.

The dimensions drawn on the shape are Top Width (above the top edge), Bottom Width (below the bottom edge) and Height (vertical, beside the right side). They are measured between the sharp corners, so they read the same with or without a fillet. Fillet R is drawn on the top left corner and is hidden when Fillet R is 0.

Limits and errors

The property page shows the red line Warning: Cannot build shape from these parameters when the outline cannot be built. This happens when:

•Fillet R is negative.

•Fillet R is too large. The fillets at the two ends of each side must fit along that side. With Top Width above 0, each slanted side must hold two fillets, which means Fillet R ≤ Height / 2 whatever the widths. The top edge needs Fillet R ≤ Top Width × tan(top corner angle / 2) / 2, and the bottom edge needs Fillet R ≤ Bottom Width × tan(bottom corner angle / 2) / 2. The top corners are 180° minus the bottom corners. The largest usable Fillet R is the smallest of these limits. With the default sizes it is 25 mm, set by the slanted sides. With Top Width 0 the apex stays sharp, each slanted side holds only one fillet, and the bottom edge is the limit.

•Fillet R is above 0 and Height is 0 with Top Width different from Bottom Width. The outline is then flat and the corners turn back on themselves. With Height 0 and equal widths no warning is shown, but the shape has no area.

The other values are not checked. Keep Bottom Width and Height positive and Top Width zero or positive. A negative width can make the outline cross itself, and a negative Height builds the shape below the insert point.

With Top Width 0 the two top corners meet at the apex. The apex is always left sharp, so Fillet R then rounds only the two bottom corners.

Every 2D shape also has the Transform properties (Base X, Base Y, Rotation, Scale, Mirroring X) and the Polar Array properties, listed after the shape's own properties.