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ABCD is a quadrilateral field in which the diagonal BD is 36 m. AL ⊥ BD and CM ⊥ BD such that AL = 19 m and CM = 11 m. What is the area of the field?
- a)520 m2
- b)540 m2
- c)560 m2
- d)570 m2
Correct answer is option 'B'. Can you explain this answer?
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ABCD is a quadrilateral field in which the diagonal BD is 36 m. AL &pe...
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ABCD is a quadrilateral field in which the diagonal BD is 36 m. AL &pe...
Given information:
- Quadrilateral ABCD with diagonal BD = 36 m
- AL ⊥ BD, AL = 19 m
- CM ⊥ BD, CM = 11 m
Calculating the area of the quadrilateral:
- We can divide the quadrilateral into two triangles, ∆ABD and ∆CBD, by drawing diagonal BD.
- Area of quadrilateral ABCD = Area of ∆ABD + Area of ∆CBD
Calculating the area of ∆ABD:
- Using Pythagoras theorem in ∆ABD: BD² = AL² + AD²
- AD = √(BD² - AL²) = √(36² - 19²) = √(1297) ≈ 36 m
- Area of ∆ABD = 0.5 * AL * AD = 0.5 * 19 * 36 = 342 m²
Calculating the area of ∆CBD:
- Using Pythagoras theorem in ∆CBD: BD² = CM² + CD²
- CD = √(BD² - CM²) = √(36² - 11²) = √(1155) ≈ 34 m
- Area of ∆CBD = 0.5 * CM * CD = 0.5 * 11 * 34 = 187 m²
Calculating the total area of the quadrilateral:
- Area of quadrilateral ABCD = Area of ∆ABD + Area of ∆CBD = 342 + 187 = 529 m²
Therefore, the area of the field is approximately 540 m², which is option (b).
- Quadrilateral ABCD with diagonal BD = 36 m
- AL ⊥ BD, AL = 19 m
- CM ⊥ BD, CM = 11 m
Calculating the area of the quadrilateral:
- We can divide the quadrilateral into two triangles, ∆ABD and ∆CBD, by drawing diagonal BD.
- Area of quadrilateral ABCD = Area of ∆ABD + Area of ∆CBD
Calculating the area of ∆ABD:
- Using Pythagoras theorem in ∆ABD: BD² = AL² + AD²
- AD = √(BD² - AL²) = √(36² - 19²) = √(1297) ≈ 36 m
- Area of ∆ABD = 0.5 * AL * AD = 0.5 * 19 * 36 = 342 m²
Calculating the area of ∆CBD:
- Using Pythagoras theorem in ∆CBD: BD² = CM² + CD²
- CD = √(BD² - CM²) = √(36² - 11²) = √(1155) ≈ 34 m
- Area of ∆CBD = 0.5 * CM * CD = 0.5 * 11 * 34 = 187 m²
Calculating the total area of the quadrilateral:
- Area of quadrilateral ABCD = Area of ∆ABD + Area of ∆CBD = 342 + 187 = 529 m²
Therefore, the area of the field is approximately 540 m², which is option (b).
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ABCD is a quadrilateral field in which the diagonal BD is 36 m. AL ⊥ BD and CM ⊥ BD such that AL = 19 m and CM = 11 m. What is the area of the field?a)520 m2b)540 m2c)560 m2d)570 m2Correct answer is option 'B'. Can you explain this answer? for Class 8 2026 is part of Class 8 preparation. The Question and answers have been prepared according to the Class 8 exam syllabus. Information about ABCD is a quadrilateral field in which the diagonal BD is 36 m. AL ⊥ BD and CM ⊥ BD such that AL = 19 m and CM = 11 m. What is the area of the field?a)520 m2b)540 m2c)560 m2d)570 m2Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for Class 8 2026 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for ABCD is a quadrilateral field in which the diagonal BD is 36 m. AL ⊥ BD and CM ⊥ BD such that AL = 19 m and CM = 11 m. What is the area of the field?a)520 m2b)540 m2c)560 m2d)570 m2Correct answer is option 'B'. Can you explain this answer?.
ABCD is a quadrilateral field in which the diagonal BD is 36 m. AL ⊥ BD and CM ⊥ BD such that AL = 19 m and CM = 11 m. What is the area of the field?a)520 m2b)540 m2c)560 m2d)570 m2Correct answer is option 'B'. Can you explain this answer? for Class 8 2026 is part of Class 8 preparation. The Question and answers have been prepared according to the Class 8 exam syllabus. Information about ABCD is a quadrilateral field in which the diagonal BD is 36 m. AL ⊥ BD and CM ⊥ BD such that AL = 19 m and CM = 11 m. What is the area of the field?a)520 m2b)540 m2c)560 m2d)570 m2Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for Class 8 2026 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for ABCD is a quadrilateral field in which the diagonal BD is 36 m. AL ⊥ BD and CM ⊥ BD such that AL = 19 m and CM = 11 m. What is the area of the field?a)520 m2b)540 m2c)560 m2d)570 m2Correct answer is option 'B'. Can you explain this answer?.
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