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If the diagonal of a square is 12 cm, then what is the area (in cm2) of the square?
- a)72
- b)72 √2
- c)36
- d)36 √2
Correct answer is option 'A'. Can you explain this answer?
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Verified Answer
If the diagonal of a square is 12 cm, then what is the area (in cm2) ...
Diagonal of square = side x √2
Area of square = side2
ATQ,
Diagonal = 12cm
Side x √2 = 12
So, side = 12/√2
Therefore,
Area = (12/√2)2 ⇒ 144/2 ⇒ 72
Most Upvoted Answer
If the diagonal of a square is 12 cm, then what is the area (in cm2) ...
Understanding the Problem:
Given that the diagonal of a square is 12 cm, we need to find the area of the square.
Approach to Solve:
To find the area of the square, we first need to determine the side length of the square using the diagonal.
Using the Pythagorean Theorem:
- In a square, the diagonal splits the square into two right-angled triangles.
- Let the side length of the square be 'a'. Then, according to the Pythagorean theorem,
(side)² + (side)² = (diagonal)²
- Substitute the values, we get:
a² + a² = 12²
2a² = 144
a² = 72
a = √72 = 6√2 cm
Finding the Area:
- The area of a square is given by the formula: Area = side * side
- Substituting the value of 'a', we get:
Area = 6√2 * 6√2 = 36 * 2 = 72 cm²
Therefore, the area of the square is 72 cm², which is option 'A'.
Given that the diagonal of a square is 12 cm, we need to find the area of the square.
Approach to Solve:
To find the area of the square, we first need to determine the side length of the square using the diagonal.
Using the Pythagorean Theorem:
- In a square, the diagonal splits the square into two right-angled triangles.
- Let the side length of the square be 'a'. Then, according to the Pythagorean theorem,
(side)² + (side)² = (diagonal)²
- Substitute the values, we get:
a² + a² = 12²
2a² = 144
a² = 72
a = √72 = 6√2 cm
Finding the Area:
- The area of a square is given by the formula: Area = side * side
- Substituting the value of 'a', we get:
Area = 6√2 * 6√2 = 36 * 2 = 72 cm²
Therefore, the area of the square is 72 cm², which is option 'A'.
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If the diagonal of a square is 12 cm, then what is the area (in cm2) of the square?a)72b)72 √2c)36d)36 √2Correct answer is option 'A'. Can you explain this answer?
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