Welcome to Westonci.ca, where your questions are met with accurate answers from a community of experts and enthusiasts. Experience the ease of finding reliable answers to your questions from a vast community of knowledgeable experts. Experience the convenience of finding accurate answers to your questions from knowledgeable experts on our platform.
Sagot :
To solve for the area of a square given its diagonal, let's follow these steps:
1. Understand the relation between the side and the diagonal:
- In a square, if the length of the diagonal is [tex]\( x \)[/tex] units, we know that each side of the square is [tex]\( s \)[/tex] units.
- The relationship between the side length [tex]\( s \)[/tex] and the diagonal [tex]\( x \)[/tex] in a square is derived from the Pythagorean theorem. For a square with side length [tex]\( s \)[/tex], the diagonal forms a right triangle with the two sides of the square.
- Therefore, [tex]\( x^2 = s^2 + s^2 \)[/tex].
2. Apply the Pythagorean theorem:
- This simplifies to [tex]\( x^2 = 2s^2 \)[/tex].
- Solving for [tex]\( s^2 \)[/tex], we get: [tex]\( s^2 = \frac{x^2}{2} \)[/tex].
3. Calculate the area of the square:
- The area of a square is given by the side length squared. So, [tex]\( \text{Area} = s^2 \)[/tex].
- Substituting [tex]\( s^2 \)[/tex] from the above equation, we have [tex]\( \text{Area} = \frac{x^2}{2} \)[/tex].
Therefore, the area of the square in terms of the diagonal [tex]\( x \)[/tex] is [tex]\(\frac{1}{2} x^2 \)[/tex] square units.
Hence, the correct answer is [tex]\(\frac{1}{2} x^2\)[/tex] square units.
1. Understand the relation between the side and the diagonal:
- In a square, if the length of the diagonal is [tex]\( x \)[/tex] units, we know that each side of the square is [tex]\( s \)[/tex] units.
- The relationship between the side length [tex]\( s \)[/tex] and the diagonal [tex]\( x \)[/tex] in a square is derived from the Pythagorean theorem. For a square with side length [tex]\( s \)[/tex], the diagonal forms a right triangle with the two sides of the square.
- Therefore, [tex]\( x^2 = s^2 + s^2 \)[/tex].
2. Apply the Pythagorean theorem:
- This simplifies to [tex]\( x^2 = 2s^2 \)[/tex].
- Solving for [tex]\( s^2 \)[/tex], we get: [tex]\( s^2 = \frac{x^2}{2} \)[/tex].
3. Calculate the area of the square:
- The area of a square is given by the side length squared. So, [tex]\( \text{Area} = s^2 \)[/tex].
- Substituting [tex]\( s^2 \)[/tex] from the above equation, we have [tex]\( \text{Area} = \frac{x^2}{2} \)[/tex].
Therefore, the area of the square in terms of the diagonal [tex]\( x \)[/tex] is [tex]\(\frac{1}{2} x^2 \)[/tex] square units.
Hence, the correct answer is [tex]\(\frac{1}{2} x^2\)[/tex] square units.
Thank you for visiting our platform. We hope you found the answers you were looking for. Come back anytime you need more information. We appreciate your visit. Our platform is always here to offer accurate and reliable answers. Return anytime. Thank you for choosing Westonci.ca as your information source. We look forward to your next visit.