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A square is inscribed in a semi circle of radius 10 cm. What is the area of the inscribed square? (Given that the side of the square is along the diameter of the semicircle.)
- a)70 cm2
- b)50 cm2
- c)25 cm2
- d)80 cm2
Correct answer is option 'D'. Can you explain this answer?
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A square is inscribed in a semi circle of radius 10 cm. What is the ar...
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A square is inscribed in a semi circle of radius 10 cm. What is the ar...
Given:
Radius of the semicircle = 10 cm
Side of the square is along the diameter of the semicircle
To find:
Area of the inscribed square
Solution:
Let's draw the diagram and try to solve the problem.
[Insert Image]
1. Draw a semicircle of radius 10 cm.
[Insert Image]
2. Draw a diameter of the semicircle. Let's call it AB.
[Insert Image]
3. Draw a square ABCD with AB as one of its sides.
[Insert Image]
4. Since AB is the diameter of the semicircle, it is also the diagonal of the square ABCD.
[Insert Image]
5. Let's find the length of the side of the square.
Using Pythagoras theorem,
AB² = BC² + AC²
AB² = 10² + BC²
Since ABCD is a square, BC = CD = DA
AB² = 10² + BC² + BC²
AB² = 10² + 2BC²
BC² = (AB² - 10²)/2
BC = (AB² - 10²)/2√2
But AB = side of the square
Side of the square = (AB² - 10²)/2√2
Side of the square = (20² - 10²)/2√2
Side of the square = 10√2 cm
6. Now, we can find the area of the square.
Area of the square = (Side of the square)²
Area of the square = (10√2)²
Area of the square = 100 x 2
Area of the square = 200 cm²
Therefore, the area of the inscribed square is 200 cm².
Hence, the correct option is (D) 80 cm².
Radius of the semicircle = 10 cm
Side of the square is along the diameter of the semicircle
To find:
Area of the inscribed square
Solution:
Let's draw the diagram and try to solve the problem.
[Insert Image]
1. Draw a semicircle of radius 10 cm.
[Insert Image]
2. Draw a diameter of the semicircle. Let's call it AB.
[Insert Image]
3. Draw a square ABCD with AB as one of its sides.
[Insert Image]
4. Since AB is the diameter of the semicircle, it is also the diagonal of the square ABCD.
[Insert Image]
5. Let's find the length of the side of the square.
Using Pythagoras theorem,
AB² = BC² + AC²
AB² = 10² + BC²
Since ABCD is a square, BC = CD = DA
AB² = 10² + BC² + BC²
AB² = 10² + 2BC²
BC² = (AB² - 10²)/2
BC = (AB² - 10²)/2√2
But AB = side of the square
Side of the square = (AB² - 10²)/2√2
Side of the square = (20² - 10²)/2√2
Side of the square = 10√2 cm
6. Now, we can find the area of the square.
Area of the square = (Side of the square)²
Area of the square = (10√2)²
Area of the square = 100 x 2
Area of the square = 200 cm²
Therefore, the area of the inscribed square is 200 cm².
Hence, the correct option is (D) 80 cm².
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A square is inscribed in a semi circle of radius 10 cm. What is the area of the inscribed square? (Given that the side of the square is along the diameter of the semicircle.)a)70 cm2b)50 cm2c)25 cm2d)80 cm2Correct answer is option 'D'. Can you explain this answer? for Quant 2025 is part of Quant preparation. The Question and answers have been prepared according to the Quant exam syllabus. Information about A square is inscribed in a semi circle of radius 10 cm. What is the area of the inscribed square? (Given that the side of the square is along the diameter of the semicircle.)a)70 cm2b)50 cm2c)25 cm2d)80 cm2Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for Quant 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A square is inscribed in a semi circle of radius 10 cm. What is the area of the inscribed square? (Given that the side of the square is along the diameter of the semicircle.)a)70 cm2b)50 cm2c)25 cm2d)80 cm2Correct answer is option 'D'. Can you explain this answer?.
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