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ABCD is a rectangle point E and FR on the side AB such that they trisect AB is the difference between the areas of trapezium CDEF and triangle ADE is 12 cm². Then what is the area of rectangle ABCD?
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ABCD is a rectangle point E and FR on the side AB such that they trise...
To solve this problem, let's break it down into smaller steps:
1. Let's assume the length of AB is 'x' units. Therefore, AE = EB = FR = RF = x/3 units.
2. The area of rectangle ABCD is given by the formula: Area = length * width. Since the length of the rectangle is x units and the width is AE (which is x/3 units), the area of the rectangle is (x)(x/3) = x^2/3 square units.
3. The area of trapezium CDEF can be calculated as the sum of the areas of triangles ADE and FEB, and the rectangle ABCD.
4. The area of triangle ADE can be calculated using the formula: Area = (base * height) / 2. The base of triangle ADE is AE = x/3 units, and the height is AD = x units. Therefore, the area of triangle ADE is (x/3)(x)/2 = x^2/6 square units.
5. The area of triangle FEB can be calculated in the same way. The base of triangle FEB is FR = x/3 units, and the height is EB = x/3 units. Therefore, the area of triangle FEB is (x/3)(x/3)/2 = x^2/18 square units.
6. The area of rectangle ABCD is already calculated as x^2/3 square units.
7. Therefore, the area of trapezium CDEF is the sum of the areas of triangles ADE and FEB, and the rectangle ABCD: (x^2/6) + (x^2/18) + (x^2/3) = (3x^2 + x^2 + 6x^2)/18 = (10x^2)/18 = (5x^2)/9 square units.
8. The difference between the areas of trapezium CDEF and triangle ADE is given as 12 cm². Therefore, we have the equation: ((5x^2)/9) - (x^2/6) = 12.
9. Solving the equation, we get: (10x^2 - 3x^2)/18 = 12 => 7x^2/18 = 12 => 7x^2 = 216 => x^2 = 216/7.
10. Therefore, the area of rectangle ABCD is x^2/3 = (216/7)/3 = 72/7 square units.
So, the area of rectangle ABCD is 72/7 square units.
1. Let's assume the length of AB is 'x' units. Therefore, AE = EB = FR = RF = x/3 units.
2. The area of rectangle ABCD is given by the formula: Area = length * width. Since the length of the rectangle is x units and the width is AE (which is x/3 units), the area of the rectangle is (x)(x/3) = x^2/3 square units.
3. The area of trapezium CDEF can be calculated as the sum of the areas of triangles ADE and FEB, and the rectangle ABCD.
4. The area of triangle ADE can be calculated using the formula: Area = (base * height) / 2. The base of triangle ADE is AE = x/3 units, and the height is AD = x units. Therefore, the area of triangle ADE is (x/3)(x)/2 = x^2/6 square units.
5. The area of triangle FEB can be calculated in the same way. The base of triangle FEB is FR = x/3 units, and the height is EB = x/3 units. Therefore, the area of triangle FEB is (x/3)(x/3)/2 = x^2/18 square units.
6. The area of rectangle ABCD is already calculated as x^2/3 square units.
7. Therefore, the area of trapezium CDEF is the sum of the areas of triangles ADE and FEB, and the rectangle ABCD: (x^2/6) + (x^2/18) + (x^2/3) = (3x^2 + x^2 + 6x^2)/18 = (10x^2)/18 = (5x^2)/9 square units.
8. The difference between the areas of trapezium CDEF and triangle ADE is given as 12 cm². Therefore, we have the equation: ((5x^2)/9) - (x^2/6) = 12.
9. Solving the equation, we get: (10x^2 - 3x^2)/18 = 12 => 7x^2/18 = 12 => 7x^2 = 216 => x^2 = 216/7.
10. Therefore, the area of rectangle ABCD is x^2/3 = (216/7)/3 = 72/7 square units.
So, the area of rectangle ABCD is 72/7 square units.
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ABCD is a rectangle point E and FR on the side AB such that they trisect AB is the difference between the areas of trapezium CDEF and triangle ADE is 12 cm². Then what is the area of rectangle ABCD?
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ABCD is a rectangle point E and FR on the side AB such that they trisect AB is the difference between the areas of trapezium CDEF and triangle ADE is 12 cm². Then what is the area of rectangle ABCD? for CAT 2024 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about ABCD is a rectangle point E and FR on the side AB such that they trisect AB is the difference between the areas of trapezium CDEF and triangle ADE is 12 cm². Then what is the area of rectangle ABCD? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for ABCD is a rectangle point E and FR on the side AB such that they trisect AB is the difference between the areas of trapezium CDEF and triangle ADE is 12 cm². Then what is the area of rectangle ABCD?.
ABCD is a rectangle point E and FR on the side AB such that they trisect AB is the difference between the areas of trapezium CDEF and triangle ADE is 12 cm². Then what is the area of rectangle ABCD? for CAT 2024 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about ABCD is a rectangle point E and FR on the side AB such that they trisect AB is the difference between the areas of trapezium CDEF and triangle ADE is 12 cm². Then what is the area of rectangle ABCD? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for ABCD is a rectangle point E and FR on the side AB such that they trisect AB is the difference between the areas of trapezium CDEF and triangle ADE is 12 cm². Then what is the area of rectangle ABCD?.
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