All Courses
Explore Courses UPSC Exam UPSC Test Series Free Notes EduRev Infinity Get the App Login Join for Free
Sign in Open App
CAT Exam  >  CAT Questions  >   Find the area of the quadrilateral formed by... Start Learning for Free
SaveJoin the Discussion on the App
Find the area of the quadrilateral formed by the points (1, 2), (6, 2), (5, – 2) and (4, – 3).
  • a)
    14 sq. units
  • b)
    20 sq. units
  • c)
    25 sq. units
  • d)
    16 sq. units
Correct answer is option 'A'. Can you explain this answer?
FREE This question is part of
Download PDF Attempt Test
Download PDF Attempt this Test
Most Upvoted Answer
Find the area of the quadrilateral formed by the points (1, 2), (6, 2...
Let A(1, 2), B(6, 2), C(5, – 2) and D(4, – 3) form a quadrilateral as shown in the figure below
So, area of ABCD = area of ΔABC + area of ΔACD
sq units = (10 + 4) sq. units
= 14 sq. units
Free Test
FREE
Start Free Test
Start Free Test
Community Answer
Find the area of the quadrilateral formed by the points (1, 2), (6, 2...
To find the area of the quadrilateral formed by the given points, we can use the Shoelace formula. The Shoelace formula, also known as the Gauss area formula or the surveyor's formula, is a method of calculating the area of a simple polygon given the coordinates of its vertices.

The Shoelace formula states that the area of a polygon with vertices (x1, y1), (x2, y2), ..., (xn, yn) is given by the formula:

Area = (1/2) * |(x1y2 + x2y3 + ... + xny1) - (x2y1 + x3y2 + ... + x1yn)|

Let's calculate the area using the given points:

Point 1: (1, 2)
Point 2: (6, 2)
Point 3: (5, -2)
Point 4: (4, -3)

Calculating the area using the Shoelace formula:

Area = (1/2) * |(1*2 + 6*(-2) + 5*(-3) + 4*2) - (2*6 + 2*5 + (-2)*4 + (-3)*1)|
= (1/2) * |(2 - 12 - 15 + 8) - (12 + 10 - 8 - 3)|
= (1/2) * |(-17) - (11)|
= (1/2) * |-28|
= 14 sq. units

Therefore, the area of the quadrilateral formed by the given points is 14 square units. Hence, option A is the correct answer.
Attention CAT Students!
To make sure you are not studying endlessly, EduRev has designed CAT study material, with Structured Courses, Videos, & Test Series. Plus get personalized analysis, doubt solving and improvement plans to achieve a great score in CAT.
< Previous Question Next Question >
Explore Courses for CAT exam

Similar CAT Doubts

Legrand Casino recently purchased a slot machine; a gaming machine, which had a main unit and five sub-units, labeled as Alpha, Gamma, Beta, Theta and Omega. The main as well as each of the sub-units had five slots, labeled as Red, Blue, Grey, Black and Yellow. The game with this slotting machine involved punching the right coin in the right slot in the right sequence i.e. one after another. For example, if coin number 3 is punched into slot Blue in Gamma sub-unit and if the main unit also pushes the coin to Blue slot, then the punch is said to be a winning shot. If the coin in the sub-unit is punched into the right slot when compared to the corresponding coin in the main unit, then the player gets Rs. 1,000 as reward. On the other hand, if the slots do not match then the player loses Rs. 333. Each player gets 25 coins to play.However, after a couple of days this slotting machine developed a peculiar problem. In the sub-units irrespective of the slot you intended to put in the coin, the sub-unit pushed the coin into the slot it wanted to every time on its own.To find out which slots in the sub-units had developed the snag, the technician played on all the sub-units using 25 coins in each of the sub-units.After some kind of analysis he found that the main machine and each of the sub-units could identify right slots for 15 coins, however for the balance of 10 coins listed below, each of the sub-units assumed different positions as right slots when compared to the main unit whose allocation of slots was the benchmark for performance of other sub-units.On playing with these sub-units, the technician earned Rs. 17,000, Rs. 11,660, Rs. 18,330, Rs. 14,330 and Rs. 18,330 respectively from each of Alpha, Gamma, Beta, Theta and Omega. All the amount being rounded off to previous tens figure. Of the ten slots which had developed the snag, there was atleast one sub-unit which identified the right slot for exactly 9 of the 10 slots.The table below gives the slots identified by each of the sub-units as right slots for the 10 problematic coins.Q. Which of these can never be a valid combination of correctly slotted coin numbers for the Alpha sub-unit?

Legrand Casino recently purchased a slot machine; a gaming machine, which had the main unit and five sub-units, labeled as Alpha, Gamma, Beta, Theta and Omega. The main, as well as each of the sub-units, had five slots, labeled as Red, Blue, Grey, Black, and Yellow. The game with this slotting machine involved punching the right coin in the right slot in the right sequence i.e. one after another. For example, if coin number 3 is punched into slot Blue in Gamma sub-unit and if the main unit also pushes the coin to Blue slot, then the punch is said to be a winning shot. If the coin in the sub-unit is punched into the right slot when compared to the corresponding coin in the main unit, then the player gets Rs. 1,000 as reward. On the other hand, if the slots do not match then the player loses Rs. 333. Each player gets 25 coins to play.However, after a couple of days, this slotting machine developed a peculiar problem. In the sub-units irrespective of the slot you intended to put in the coin, the sub-unit pushed the coin into the slot it wanted to every time on its own.To find out which slots in the sub-units had developed the snag, the technician played on all the sub-units using 25 coins in each of the sub-units.After some kind of analysis he found that the main machine and each of the sub-units could identify right slots for 15 coins, however for the balance of 10 coins listed below, each of the sub-units assumed different positions as right slots when compared to the main unit whose allocation of slots was the benchmark for performance of other sub-units.On playing with these sub-units, the technician earned Rs. 17,000, Rs. 11,660, Rs. 18,330, Rs. 14,330 and Rs. 18,330 respectively from each of Alpha, Gamma, Beta, Theta and Omega. All the amount being rounded off to previous tens figure. Of the ten slots which had developed the snag, there was at least one sub-unit which identified the right slot for exactly 9 of the 10 slots.The table below gives the slots identified by each of the sub-units as right slots for the 10 problematic coins.For the 10 incorrectly slotted coins, how many slots were commonly and correctly identified by more than 1 sub-unit?

Legrand Casino recently purchased a slot machine; a gaming machine, which had the main unit and five sub-units, labeled as Alpha, Gamma, Beta, Theta and Omega. The main, as well as each of the sub-units, had five slots, labeled as Red, Blue, Grey, Black, and Yellow. The game with this slotting machine involved punching the right coin in the right slot in the right sequence i.e. one after another. For example, if coin number 3 is punched into slot Blue in Gamma sub-unit and if the main unit also pushes the coin to Blue slot, then the punch is said to be a winning shot. If the coin in the sub-unit is punched into the right slot when compared to the corresponding coin in the main unit, then the player gets Rs. 1,000 as reward. On the other hand, if the slots do not match then the player loses Rs. 333. Each player gets 25 coins to play.However, after a couple of days, this slotting machine developed a peculiar problem. In the sub-units irrespective of the slot you intended to put in the coin, the sub-unit pushed the coin into the slot it wanted to every time on its own.To find out which slots in the sub-units had developed the snag, the technician played on all the sub-units using 25 coins in each of the sub-units.After some kind of analysis he found that the main machine and each of the sub-units could identify right slots for 15 coins, however for the balance of 10 coins listed below, each of the sub-units assumed different positions as right slots when compared to the main unit whose allocation of slots was the benchmark for performance of other sub-units.On playing with these sub-units, the technician earned Rs. 17,000, Rs. 11,660, Rs. 18,330, Rs. 14,330 and Rs. 18,330 respectively from each of Alpha, Gamma, Beta, Theta and Omega. All the amount being rounded off to previous tens figure. Of the ten slots which had developed the snag, there was at least one sub-unit which identified the right slot for exactly 9 of the 10 slots.The table below gives the slots identified by each of the sub-units as right slots for the 10 problematic coins.What is the median value of the number of incorrect slots individually identified by the 5 sub-units?

Top Courses for CATView all

Top Courses for CAT

Find the area of the quadrilateral formed by the points (1, 2), (6, 2), (5, – 2) and (4, – 3).a)14 sq. unitsb)20 sq. unitsc)25 sq. unitsd)16 sq. unitsCorrect answer is option 'A'. Can you explain this answer?
Question Description
Find the area of the quadrilateral formed by the points (1, 2), (6, 2), (5, – 2) and (4, – 3).a)14 sq. unitsb)20 sq. unitsc)25 sq. unitsd)16 sq. unitsCorrect answer is option 'A'. Can you explain this answer? for CAT 2024 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about Find the area of the quadrilateral formed by the points (1, 2), (6, 2), (5, – 2) and (4, – 3).a)14 sq. unitsb)20 sq. unitsc)25 sq. unitsd)16 sq. unitsCorrect answer is option 'A'. Can you explain this answer? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Find the area of the quadrilateral formed by the points (1, 2), (6, 2), (5, – 2) and (4, – 3).a)14 sq. unitsb)20 sq. unitsc)25 sq. unitsd)16 sq. unitsCorrect answer is option 'A'. Can you explain this answer?.
Solutions for Find the area of the quadrilateral formed by the points (1, 2), (6, 2), (5, – 2) and (4, – 3).a)14 sq. unitsb)20 sq. unitsc)25 sq. unitsd)16 sq. unitsCorrect answer is option 'A'. Can you explain this answer? in English & in Hindi are available as part of our courses for CAT. Download more important topics, notes, lectures and mock test series for CAT Exam by signing up for free.
Here you can find the meaning of Find the area of the quadrilateral formed by the points (1, 2), (6, 2), (5, – 2) and (4, – 3).a)14 sq. unitsb)20 sq. unitsc)25 sq. unitsd)16 sq. unitsCorrect answer is option 'A'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of Find the area of the quadrilateral formed by the points (1, 2), (6, 2), (5, – 2) and (4, – 3).a)14 sq. unitsb)20 sq. unitsc)25 sq. unitsd)16 sq. unitsCorrect answer is option 'A'. Can you explain this answer?, a detailed solution for Find the area of the quadrilateral formed by the points (1, 2), (6, 2), (5, – 2) and (4, – 3).a)14 sq. unitsb)20 sq. unitsc)25 sq. unitsd)16 sq. unitsCorrect answer is option 'A'. Can you explain this answer? has been provided alongside types of Find the area of the quadrilateral formed by the points (1, 2), (6, 2), (5, – 2) and (4, – 3).a)14 sq. unitsb)20 sq. unitsc)25 sq. unitsd)16 sq. unitsCorrect answer is option 'A'. Can you explain this answer? theory, EduRev gives you an ample number of questions to practice Find the area of the quadrilateral formed by the points (1, 2), (6, 2), (5, – 2) and (4, – 3).a)14 sq. unitsb)20 sq. unitsc)25 sq. unitsd)16 sq. unitsCorrect answer is option 'A'. Can you explain this answer? tests, examples and also practice CAT tests.
Explore Courses for CAT exam

Top Courses for CAT

Explore Courses

Suggested Free Tests

Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
10M+ students study on EduRev
Get App
© 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