The Triangle

![Diagram showing an equilateral triangle with a vertical line representing the height or "center length."]

Answer: 84 square steps

Method: Take the side of 14 steps and multiply it by 6 to get 84. Divide this by 7 to find the center length the height of 12 steps. Separately, take the 14 steps of each side and halve them to get 7; multiply this by the height to match the query. This method uses the traditional Chinese approximation that the height of an equilateral triangle is 6/7ths of its side. Area = (Side/2) × (Side × 6/7).
A triangle is the same as a Gui Gui: a pointed ritual jade tablet. Multiplying half the width by the center length of 12 steps also yields the area.

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The Shuttle Shape

Shuttle shape (suo-xing): a rhombus or lozenge, named for its resemblance to a weaver's shuttle.

![Diagram of a rhombus with its two diagonals marked.]

Suppose there is a shuttle-shaped field with a center length of 52 steps and a center width of 12 steps. What is its area?

Answer: 312 square steps.

Method: Take the length of 52 steps and multiply it by the width of 12 steps to get 624 square steps. Halve this to obtain the area ji: the accumulated product or area of 312 square steps. This matches the query.
For right triangles gougu, Gui triangles, and shuttle shapes, the rule is to multiply and halve. Though the field shapes differ, the underlying logic is the same.

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Suppose there is a slanted Gui field an oblique or scalene triangle with a length of 30 steps and a width of 16 steps. What is its area?