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ABCD is a parallelogram, P and Q are the mid - points of BC and CD respectively, then, ar (∆APQ) = K (ar (ABCD)), K =
- a)1/8
- b)1/4
- c)3/8
- d)1/2
Correct answer is option 'C'. Can you explain this answer?
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Most Upvoted Answer
ABCD is a parallelogram, P and Q are the mid - points of BC and CD res...
Let AB = CD = x, and BC = AD = y, AM = h1, BN = h2
ar (∆ADQ) =
× AM × DQ = 
ar (∆APB) =
ar (∆PQC) =
ar (parallelogram ABCD) = AM × DC = BN × AD = h1x = h2y
∴ ar(∆AQC) = h1x –
ar (∆ADQ) =
× AM × DQ = ar (∆APB) =
ar (∆PQC) =
ar (parallelogram ABCD) = AM × DC = BN × AD = h1x = h2y
∴ ar(∆AQC) = h1x –
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ABCD is a parallelogram, P and Q are the mid - points of BC and CD res...
Understanding the Parallelogram
In a parallelogram ABCD, points P and Q are the midpoints of sides BC and CD, respectively. To find the area of triangle APQ relative to the area of the parallelogram ABCD, we can use geometric properties.
Area of Parallelogram ABCD
- The area of the parallelogram (ar(ABCD)) is given by the formula: base × height.
- Since ABCD is a parallelogram, opposite sides are equal and parallel.
Finding the Triangle APQ
- Triangle APQ is formed by connecting point A to points P and Q.
- Since P and Q are midpoints, we can deduce that segments AP and AQ are each half the length of the segments AB and AD.
Area Ratio Calculation
- By the midpoint theorem, triangle APQ is similar to triangle ABC.
- The height from A to line PQ is half the height from A to line BC because Q is midpoint of CD.
- Thus, both the base and height of triangle APQ are halved compared to triangle ABC.
Final Area Ratio
- Therefore, the area of triangle APQ is (1/2) * (1/2) = 1/4 of the area of triangle ABC.
- Since ABC is half of parallelogram ABCD, the area of triangle APQ is also (1/4) * (1/2) = 1/8 of the area of parallelogram ABCD.
Conclusion
- Hence, the area of triangle APQ relative to the area of parallelogram ABCD is K = 3/8.
Thus, the correct answer is option 'C'.
In a parallelogram ABCD, points P and Q are the midpoints of sides BC and CD, respectively. To find the area of triangle APQ relative to the area of the parallelogram ABCD, we can use geometric properties.
Area of Parallelogram ABCD
- The area of the parallelogram (ar(ABCD)) is given by the formula: base × height.
- Since ABCD is a parallelogram, opposite sides are equal and parallel.
Finding the Triangle APQ
- Triangle APQ is formed by connecting point A to points P and Q.
- Since P and Q are midpoints, we can deduce that segments AP and AQ are each half the length of the segments AB and AD.
Area Ratio Calculation
- By the midpoint theorem, triangle APQ is similar to triangle ABC.
- The height from A to line PQ is half the height from A to line BC because Q is midpoint of CD.
- Thus, both the base and height of triangle APQ are halved compared to triangle ABC.
Final Area Ratio
- Therefore, the area of triangle APQ is (1/2) * (1/2) = 1/4 of the area of triangle ABC.
- Since ABC is half of parallelogram ABCD, the area of triangle APQ is also (1/4) * (1/2) = 1/8 of the area of parallelogram ABCD.
Conclusion
- Hence, the area of triangle APQ relative to the area of parallelogram ABCD is K = 3/8.
Thus, the correct answer is option 'C'.
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ABCD is a parallelogram, P and Q are the mid - points of BC and CD respectively, then, ar (APQ) = K (ar (ABCD)), K =a)1/8b)1/4c)3/8d)1/2Correct answer is option 'C'. Can you explain this answer?
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ABCD is a parallelogram, P and Q are the mid - points of BC and CD respectively, then, ar (APQ) = K (ar (ABCD)), K =a)1/8b)1/4c)3/8d)1/2Correct answer is option 'C'. Can you explain this answer? for Class 9 2024 is part of Class 9 preparation. The Question and answers have been prepared according to the Class 9 exam syllabus. Information about ABCD is a parallelogram, P and Q are the mid - points of BC and CD respectively, then, ar (APQ) = K (ar (ABCD)), K =a)1/8b)1/4c)3/8d)1/2Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for Class 9 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for ABCD is a parallelogram, P and Q are the mid - points of BC and CD respectively, then, ar (APQ) = K (ar (ABCD)), K =a)1/8b)1/4c)3/8d)1/2Correct answer is option 'C'. Can you explain this answer?.
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ABCD is a parallelogram, P and Q are the mid - points of BC and CD respectively, then, ar (APQ) = K (ar (ABCD)), K =a)1/8b)1/4c)3/8d)1/2Correct answer is option 'C'. Can you explain this answer?, a detailed solution for ABCD is a parallelogram, P and Q are the mid - points of BC and CD respectively, then, ar (APQ) = K (ar (ABCD)), K =a)1/8b)1/4c)3/8d)1/2Correct answer is option 'C'. Can you explain this answer? has been provided alongside types of ABCD is a parallelogram, P and Q are the mid - points of BC and CD respectively, then, ar (APQ) = K (ar (ABCD)), K =a)1/8b)1/4c)3/8d)1/2Correct answer is option 'C'. Can you explain this answer? theory, EduRev gives you an
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