Answer: 2,304 square steps.

Method: Set down the southern and northern widths and add them together to get 72 steps. Halve this to get 36 steps. Multiply this by the length of 64 steps to find the area original: "積" (jī) — literally "accumulation," referring to the total area. This matches the query.

The Oblique Shape

Oblique shape (xié xíng): often used interchangeably with a trapezoid where the sides are slanted.

South width: 32 steps Length: 64 steps North width: 40 steps

Suppose there is an eyebrow-shaped field original: "méi tián" — a field shaped like a crescent or a segment of a circular ring with an upper circumference of 40 steps, a lower circumference of 30 steps, and a diameter meaning the vertical width or height of the crescent of 8 steps. Ask: what is the area?

The Eyebrow Shape

The ancient methods are the authority, yet there is a discrepancy with calculations today. This likely refers to the "ancient" value of Pi (3) versus more precise contemporary values used to calculate arcs.

Borrow the lower chord to construct the upper chord; only then can the sought-after lower chord be obtained. A technical instruction for geometric construction of the arc segment.

Diameter: 8 steps Circumference: 40 steps Lower circumference: 30 steps

Answer: 140 square steps.

Method: Set down the upper and lower circumferences and add them together to get 70 steps. Halve this to get 35 steps. Separately, take the diameter of 8 steps and halve it to get 4 steps. Multiply [the first result] by these [4 steps] to find the area. This matches the query.

Suppose there is an ox-horn-shaped field original: "niújiǎo tián" — a field resembling a curved, tapering triangle where the length along the curve original: "yī wān cháng" is 17.5 steps and the width is 8 steps. Ask: what is the area?

The vocabulary below serves as a reference for the technical terms used in the diagrams and problems above.
Oblique shape (xié xíng), Eyebrow shape (méi xíng), Ox-horn field (niújiǎo tián), Width (guǎng), Length/Height (zòng), Diameter/Vertical width (jìng), Circumference/Arc length (zhōu), Area (jī), South width (nán guǎng), North width (běi guǎng)