Find the area of a square if its diagonal is 20.
| May 9, 2021 | education
1. Vertices of the square – A, B, C, D. Diagonal AC = 20 units. S is the area of the square.
2. We take as x the length of the side of the square.
3. Considering that the sides of the square are equal, we compose the equation:
х² + х² = АС² = 20² = 400 units of measurement².
2x² = 400 units of measurement².
х² = 200 units of measurement².
x = √200 = √100 x 2 = 10√2.
Each side of a square is equal to 10√2 units of measurement.
4. S = х² = 200 units of measurement².
Answer: S equals 200 units².
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