What is the total area of a square land plot possessing a diagonal length of 20 m?
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Answer: C. 200 sq m
Explanation
The area of a square expressed in terms of its diagonal length is calculated by squaring the diagonal and dividing by two. Squaring a diagonal length of 20 meters gives 400 square meters for the squared diagonal value. Dividing 400 by two results in a total land area of exactly 200 square meters. A square is a regular quadrilateral with four equal sides and internal right angles. The diagonals of a square are equal in length and intersect perpendicularly at their midpoints. Using the diagonal formula bypasses the need to calculate individual side lengths when finding square area.
Land surveyors and real estate professionals often measure plot diagonals when direct side access is obstructed. Construction layout planning uses diagonal measurements to verify square corners and total plot areas. This geometry concept simplifies area calculations for square plots and architectural floor plans. Option A overestimates the total land area by using an incorrect formula multiplier. Option B results from an arithmetic error during the diagonal squaring and division process. Option D represents the squared diagonal value itself before dividing by the required factor of two.
- Subject
- Mathematics
- Category
- Mathematics
- Topic
- —
- Difficulty
- medium
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