Question 2707: Area of a Half-Open Integer-Endpoint Rectangle

Original question and givens

Use one equal-unit orthonormal Euclidean Cartesian frame. For the half-open rectangle [-10, -7)×[-6, 1), find the exact area in squared length units.

• G001 — Use one equal-unit orthonormal Euclidean Cartesian frame. For the half-open rectangle [-10, -7)×[-6, 1), find the exact area in squared length units.

Definition and scope

Use the original question domain, assumptions and cited MKO definitions. This item has second-context mathematical and bilingual review, with the model, answer and every arithmetic step independently recomputed from the original parameters; the source question remains a candidate.

• mko-area

Step-by-step derivation

orthonormal equal-length coordinate units;half-open regions

area in squared length units

coordinate rectangle width := sub(-7, -10)

coordinate rectangle width = 3

coordinate rectangle height := sub(1, -6)

coordinate rectangle height = 7

coordinate rectangle area := mul(3, 7)

coordinate rectangle area = 21

[-10, -7, -6, 1]

area=21

Reverse checks

• S005 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
• S004 · premise_and_result_audit — Recompute coordinate rectangle area with exact rational arithmetic, not rounded decimals.
• S003 · premise_and_result_audit — Recompute coordinate rectangle height with exact rational arithmetic, not rounded decimals.
• S002 · premise_and_result_audit — Recompute coordinate rectangle width with exact rational arithmetic, not rounded decimals.
• S001 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.

Result

21

The full substitutions and premise checks give the original answer; source identity,format and status are unchanged.

This question review and source binding

Review date: 2026-10-26

Original questions, answers, step expressions, numeric ASTs and historical records are retained. Source candidate labels remain historical and are not overwritten as formal proof.