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How can I create a rectangle trapezium due to the height, base and inclination of the oblique side?

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Here's one method that might work for you.

  1. Draw a rectangle, set the width and height as required.

  2. Copy it.

  3. Skew it by the desired angle.

  4. Paste the copy, and with snapping enabled, move it so that the corners align.

  5. Select both shapes, click Path > Division

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  1. Draw a rectangle using your wanted base and height You can enter numeric width and height.

  2. Draw a horizontal line. Use the pen and hold the Ctrl key to get it horizontal

  3. Select the line and goto Object > Transform to rotate the line to the wanted inclination. Here the rotation is 66 degrees

  4. Move the line starting from a bottom corner of the rectangle. Have at least endpoint and cusp point snaps on, no snap to grid!

  5. Select the rectangle. Goto Path > Object to path. This makes the rectangle to freely editable path. Take the Node editing tool. Hold the Ctrl key and move the corner to the crossing point with the line. Have the appropriate snapping on.

  6. Remove the line. Done.

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