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In a quadrilateral, the length of one of its diagonal is 23 cm and the perpendiculars drawn on this diagonal from other two vertices measure 17 cm and 7 cm respectively. Find the area of the quadrilateral.
- a)225 cm2
- b)149 cm2
- c)276 cm2
- d)136 cm2
Correct answer is option 'C'. Can you explain this answer?
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In a quadrilateral, the length of one of its diagonal is 23 cm and the...
Area of quadrilateral 
any diagonal × (sum of perpendiculars drawn on diagonal from two vertices)
any diagonal × (sum of perpendiculars drawn on diagonal from two vertices)Most Upvoted Answer
In a quadrilateral, the length of one of its diagonal is 23 cm and the...
To find the area of the quadrilateral, we can divide it into two triangles and then calculate the sum of their areas.
1. Divide the quadrilateral:
Draw the perpendiculars from the two vertices on the diagonal. This will divide the quadrilateral into two triangles.
2. Calculate the area of the first triangle:
The first triangle is formed by the diagonal, the perpendicular of length 17 cm, and a side of the quadrilateral. We can use the formula for the area of a triangle, which is 1/2 * base * height.
In this triangle, the base is the diagonal of length 23 cm, and the height is the perpendicular of length 17 cm. Therefore, the area of the first triangle is 1/2 * 23 cm * 17 cm = 195.5 cm^2.
3. Calculate the area of the second triangle:
The second triangle is formed by the diagonal, the perpendicular of length 7 cm, and the other side of the quadrilateral. Using the same formula for the area of a triangle, we can calculate its area.
In this triangle, the base is still the diagonal of length 23 cm, and the height is the perpendicular of length 7 cm. Therefore, the area of the second triangle is 1/2 * 23 cm * 7 cm = 80.5 cm^2.
4. Calculate the total area of the quadrilateral:
To find the total area of the quadrilateral, we need to sum the areas of the two triangles. Adding the area of the first triangle (195.5 cm^2) and the area of the second triangle (80.5 cm^2), we get a total area of 276 cm^2.
Therefore, the correct answer is option C) 276 cm^2.
1. Divide the quadrilateral:
Draw the perpendiculars from the two vertices on the diagonal. This will divide the quadrilateral into two triangles.
2. Calculate the area of the first triangle:
The first triangle is formed by the diagonal, the perpendicular of length 17 cm, and a side of the quadrilateral. We can use the formula for the area of a triangle, which is 1/2 * base * height.
In this triangle, the base is the diagonal of length 23 cm, and the height is the perpendicular of length 17 cm. Therefore, the area of the first triangle is 1/2 * 23 cm * 17 cm = 195.5 cm^2.
3. Calculate the area of the second triangle:
The second triangle is formed by the diagonal, the perpendicular of length 7 cm, and the other side of the quadrilateral. Using the same formula for the area of a triangle, we can calculate its area.
In this triangle, the base is still the diagonal of length 23 cm, and the height is the perpendicular of length 7 cm. Therefore, the area of the second triangle is 1/2 * 23 cm * 7 cm = 80.5 cm^2.
4. Calculate the total area of the quadrilateral:
To find the total area of the quadrilateral, we need to sum the areas of the two triangles. Adding the area of the first triangle (195.5 cm^2) and the area of the second triangle (80.5 cm^2), we get a total area of 276 cm^2.
Therefore, the correct answer is option C) 276 cm^2.
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In a quadrilateral, the length of one of its diagonal is 23 cm and the perpendiculars drawn on this diagonal from other two vertices measure 17 cm and 7 cm respectively. Find the area of the quadrilateral.a)225 cm2b)149 cm2c)276 cm2d)136 cm2Correct answer is option 'C'. Can you explain this answer?
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In a quadrilateral, the length of one of its diagonal is 23 cm and the perpendiculars drawn on this diagonal from other two vertices measure 17 cm and 7 cm respectively. Find the area of the quadrilateral.a)225 cm2b)149 cm2c)276 cm2d)136 cm2Correct answer is option 'C'. Can you explain this answer? for Class 7 2024 is part of Class 7 preparation. The Question and answers have been prepared according to the Class 7 exam syllabus. Information about In a quadrilateral, the length of one of its diagonal is 23 cm and the perpendiculars drawn on this diagonal from other two vertices measure 17 cm and 7 cm respectively. Find the area of the quadrilateral.a)225 cm2b)149 cm2c)276 cm2d)136 cm2Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for Class 7 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for In a quadrilateral, the length of one of its diagonal is 23 cm and the perpendiculars drawn on this diagonal from other two vertices measure 17 cm and 7 cm respectively. Find the area of the quadrilateral.a)225 cm2b)149 cm2c)276 cm2d)136 cm2Correct answer is option 'C'. Can you explain this answer?.
In a quadrilateral, the length of one of its diagonal is 23 cm and the perpendiculars drawn on this diagonal from other two vertices measure 17 cm and 7 cm respectively. Find the area of the quadrilateral.a)225 cm2b)149 cm2c)276 cm2d)136 cm2Correct answer is option 'C'. Can you explain this answer? for Class 7 2024 is part of Class 7 preparation. The Question and answers have been prepared according to the Class 7 exam syllabus. Information about In a quadrilateral, the length of one of its diagonal is 23 cm and the perpendiculars drawn on this diagonal from other two vertices measure 17 cm and 7 cm respectively. Find the area of the quadrilateral.a)225 cm2b)149 cm2c)276 cm2d)136 cm2Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for Class 7 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for In a quadrilateral, the length of one of its diagonal is 23 cm and the perpendiculars drawn on this diagonal from other two vertices measure 17 cm and 7 cm respectively. Find the area of the quadrilateral.a)225 cm2b)149 cm2c)276 cm2d)136 cm2Correct answer is option 'C'. Can you explain this answer?.
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In a quadrilateral, the length of one of its diagonal is 23 cm and the perpendiculars drawn on this diagonal from other two vertices measure 17 cm and 7 cm respectively. Find the area of the quadrilateral.a)225 cm2b)149 cm2c)276 cm2d)136 cm2Correct answer is option 'C'. Can you explain this answer?, a detailed solution for In a quadrilateral, the length of one of its diagonal is 23 cm and the perpendiculars drawn on this diagonal from other two vertices measure 17 cm and 7 cm respectively. Find the area of the quadrilateral.a)225 cm2b)149 cm2c)276 cm2d)136 cm2Correct answer is option 'C'. Can you explain this answer? has been provided alongside types of In a quadrilateral, the length of one of its diagonal is 23 cm and the perpendiculars drawn on this diagonal from other two vertices measure 17 cm and 7 cm respectively. Find the area of the quadrilateral.a)225 cm2b)149 cm2c)276 cm2d)136 cm2Correct answer is option 'C'. Can you explain this answer? theory, EduRev gives you an
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