GMAT Exam > GMAT Questions > In a rectangular coordinate plane, points A(3...
Start Learning for Free
In a rectangular coordinate plane, points A(3,4), B(6,-5), C(-4,-3) and D(-2,2) are joined to form a quadrilateral. What is the area, in square units, of quadrilateral ABCD?
- a)35
- b)37.5
- c)45
- d)52.5
- e)60
Correct answer is option 'D'. Can you explain this answer?
Verified Answer
In a rectangular coordinate plane, points A(3,4), B(6,-5), C(-4,-3) an...
Given
- The given information corresponds to the following diagram:
To Find: Area of quadrilateral ABCD
Approach
- To find the area of quadrilateral ABCD, we’ll use the method of addition and subtraction of areas.
- We will extend the quadrilateral such that it forms rectangular figures – rectangles or right-angled triangles. This can be done as under:
2. So, Area of Quadrilateral ABCD = (Area of Rectangle QBPS) – (ar ΔAPB + ar ΔBQC + ar ΔCRD + ar of square DRST + ar ΔATD)
Looking at the answer choices, we see that the correct answer is Option D
Most Upvoted Answer
In a rectangular coordinate plane, points A(3,4), B(6,-5), C(-4,-3) an...
To find the area of quadrilateral ABCD, we can divide it into two triangles, ABC and CDA, and then sum the areas of these two triangles.
Finding the area of triangle ABC:
To find the area of triangle ABC, we can use the formula for the area of a triangle given its vertices in the coordinate plane. The formula is:
Area = 0.5 * |x1(y2 - y3) + x2(y3 - y1) + x3(y1 - y2)|
For triangle ABC, the coordinates of the vertices are A(3,4), B(6,-5), and C(-4,-3). Using the formula, we can calculate the area:
Area of triangle ABC = 0.5 * |3(-5 - (-3)) + 6(-3 - 4) + (-4)(4 - (-5))|
= 0.5 * |3(-2) + 6(-7) + (-4)(9)|
= 0.5 * |-6 - 42 - 36|
= 0.5 * |-84|
= 0.5 * 84
= 42
Finding the area of triangle CDA:
To find the area of triangle CDA, we can use the same formula as above. The coordinates of the vertices are C(-4,-3), D(-2,2), and A(3,4). Calculating the area:
Area of triangle CDA = 0.5 * |-4(2 - 4) + (-2)(4 - (-3)) + 3((-3) - 2)|
= 0.5 * |-4(-2) + (-2)(7) + 3(-5)|
= 0.5 * |8 - 14 - 15|
= 0.5 * |-21|
= 0.5 * 21
= 10.5
Summing the areas of the two triangles:
To find the area of quadrilateral ABCD, we sum the areas of triangle ABC and triangle CDA:
Area of quadrilateral ABCD = Area of triangle ABC + Area of triangle CDA
= 42 + 10.5
= 52.5
Therefore, the area of quadrilateral ABCD is 52.5 square units, which corresponds to option D.
Finding the area of triangle ABC:
To find the area of triangle ABC, we can use the formula for the area of a triangle given its vertices in the coordinate plane. The formula is:
Area = 0.5 * |x1(y2 - y3) + x2(y3 - y1) + x3(y1 - y2)|
For triangle ABC, the coordinates of the vertices are A(3,4), B(6,-5), and C(-4,-3). Using the formula, we can calculate the area:
Area of triangle ABC = 0.5 * |3(-5 - (-3)) + 6(-3 - 4) + (-4)(4 - (-5))|
= 0.5 * |3(-2) + 6(-7) + (-4)(9)|
= 0.5 * |-6 - 42 - 36|
= 0.5 * |-84|
= 0.5 * 84
= 42
Finding the area of triangle CDA:
To find the area of triangle CDA, we can use the same formula as above. The coordinates of the vertices are C(-4,-3), D(-2,2), and A(3,4). Calculating the area:
Area of triangle CDA = 0.5 * |-4(2 - 4) + (-2)(4 - (-3)) + 3((-3) - 2)|
= 0.5 * |-4(-2) + (-2)(7) + 3(-5)|
= 0.5 * |8 - 14 - 15|
= 0.5 * |-21|
= 0.5 * 21
= 10.5
Summing the areas of the two triangles:
To find the area of quadrilateral ABCD, we sum the areas of triangle ABC and triangle CDA:
Area of quadrilateral ABCD = Area of triangle ABC + Area of triangle CDA
= 42 + 10.5
= 52.5
Therefore, the area of quadrilateral ABCD is 52.5 square units, which corresponds to option D.
|
Explore Courses for GMAT exam
|
|
Similar GMAT Doubts
Top Courses for GMATView all
In a rectangular coordinate plane, points A(3,4), B(6,-5), C(-4,-3) and D(-2,2) are joined to form a quadrilateral. What is the area, in square units, of quadrilateral ABCD?a)35b)37.5c)45d)52.5e)60Correct answer is option 'D'. Can you explain this answer?
Question Description
In a rectangular coordinate plane, points A(3,4), B(6,-5), C(-4,-3) and D(-2,2) are joined to form a quadrilateral. What is the area, in square units, of quadrilateral ABCD?a)35b)37.5c)45d)52.5e)60Correct answer is option 'D'. Can you explain this answer? for GMAT 2025 is part of GMAT preparation. The Question and answers have been prepared according to the GMAT exam syllabus. Information about In a rectangular coordinate plane, points A(3,4), B(6,-5), C(-4,-3) and D(-2,2) are joined to form a quadrilateral. What is the area, in square units, of quadrilateral ABCD?a)35b)37.5c)45d)52.5e)60Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for GMAT 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for In a rectangular coordinate plane, points A(3,4), B(6,-5), C(-4,-3) and D(-2,2) are joined to form a quadrilateral. What is the area, in square units, of quadrilateral ABCD?a)35b)37.5c)45d)52.5e)60Correct answer is option 'D'. Can you explain this answer?.
In a rectangular coordinate plane, points A(3,4), B(6,-5), C(-4,-3) and D(-2,2) are joined to form a quadrilateral. What is the area, in square units, of quadrilateral ABCD?a)35b)37.5c)45d)52.5e)60Correct answer is option 'D'. Can you explain this answer? for GMAT 2025 is part of GMAT preparation. The Question and answers have been prepared according to the GMAT exam syllabus. Information about In a rectangular coordinate plane, points A(3,4), B(6,-5), C(-4,-3) and D(-2,2) are joined to form a quadrilateral. What is the area, in square units, of quadrilateral ABCD?a)35b)37.5c)45d)52.5e)60Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for GMAT 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for In a rectangular coordinate plane, points A(3,4), B(6,-5), C(-4,-3) and D(-2,2) are joined to form a quadrilateral. What is the area, in square units, of quadrilateral ABCD?a)35b)37.5c)45d)52.5e)60Correct answer is option 'D'. Can you explain this answer?.
Solutions for In a rectangular coordinate plane, points A(3,4), B(6,-5), C(-4,-3) and D(-2,2) are joined to form a quadrilateral. What is the area, in square units, of quadrilateral ABCD?a)35b)37.5c)45d)52.5e)60Correct answer is option 'D'. Can you explain this answer? in English & in Hindi are available as part of our courses for GMAT.
Download more important topics, notes, lectures and mock test series for GMAT Exam by signing up for free.
Here you can find the meaning of In a rectangular coordinate plane, points A(3,4), B(6,-5), C(-4,-3) and D(-2,2) are joined to form a quadrilateral. What is the area, in square units, of quadrilateral ABCD?a)35b)37.5c)45d)52.5e)60Correct answer is option 'D'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
In a rectangular coordinate plane, points A(3,4), B(6,-5), C(-4,-3) and D(-2,2) are joined to form a quadrilateral. What is the area, in square units, of quadrilateral ABCD?a)35b)37.5c)45d)52.5e)60Correct answer is option 'D'. Can you explain this answer?, a detailed solution for In a rectangular coordinate plane, points A(3,4), B(6,-5), C(-4,-3) and D(-2,2) are joined to form a quadrilateral. What is the area, in square units, of quadrilateral ABCD?a)35b)37.5c)45d)52.5e)60Correct answer is option 'D'. Can you explain this answer? has been provided alongside types of In a rectangular coordinate plane, points A(3,4), B(6,-5), C(-4,-3) and D(-2,2) are joined to form a quadrilateral. What is the area, in square units, of quadrilateral ABCD?a)35b)37.5c)45d)52.5e)60Correct answer is option 'D'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice In a rectangular coordinate plane, points A(3,4), B(6,-5), C(-4,-3) and D(-2,2) are joined to form a quadrilateral. What is the area, in square units, of quadrilateral ABCD?a)35b)37.5c)45d)52.5e)60Correct answer is option 'D'. Can you explain this answer? tests, examples and also practice GMAT tests.
|
|
Explore Courses for GMAT exam
|
|
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
|
© EduRev
|
Education Revolution
|
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup