There was originally a rectangular field. Now, from the northeast corner, a gougu: right-angled triangle literally 'base and altitude' section is cut, with an area of 38 paces, 7 tenths, and 2 hundredths. The gu: altitude and the gou: base are equal in length. Question: What is the length of each?

Answer: The northeast sides are each 8 paces and 8 tenths.

The method states: Set the cut area of 38.72 paces and double it to obtain 77.44 paces as the shi: dividend. Use the kai pingfang: square root extraction method to divide it. This yields 8.8 paces for each of the northeast sides, which matches the question.
To verify: Multiply the base and altitude by each other and halve the result to obtain the area.

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Cutting a Right-Angled Triangle from a Rectangular Field

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Song for Cutting Areas from Trapezoidal Fields

Sloping trapezoids and right-angle cuts are fully detailed in Volume 15.

Examine the cutting of trapezoidal fields with care:
Double the area and multiply by the difference in width to find the length.
Yet use the original length as the rule the divisor,
Performing the division to process the dividend.
If cutting a section from the wide end of the field,
Square the wide width and subtract the dividend accordingly.

This mnemonic describes the "Method of Side-Cutting" for trapezoids. In traditional Chinese geometry, calculating the dimensions of a sub-section of a trapezoid often required solving a quadratic equation, here simplified into a step-by-step procedure involving the "dividend" (shi) and square roots.