CAT Exam > CAT Questions > ABCD is an isosceles trapezium such that AD |...
Start Learning for Free
ABCD is an isosceles trapezium such that AD || BC, AB = 5 cm, AD = 8 cm and BC = 14 cm. What is the area (in cm2) of trapezium?
- a)36
- b)44
- c)88
- d)144
Correct answer is option 'B'. Can you explain this answer?
| FREE This question is part of | Download PDF Attempt this Test |
Verified Answer
ABCD is an isosceles trapezium such that AD || BC, AB = 5 cm, AD = 8 c...
Let AE and DF are the perpendiculars dropped
As can be observed in figure,
BC can be divided as, BC = BE + EF + FC,
such that, EF = AD = 8 cm
and BE = FC =
= 3 cm
Solving, AE = DF =
= 4 cm
Area trapezium ABCD
As can be observed in figure,
BC can be divided as, BC = BE + EF + FC,
such that, EF = AD = 8 cm
and BE = FC =
= 3 cmSolving, AE = DF =
= 4 cmArea trapezium ABCD
► Area △ABE + Area rectangle AEFD + Area △CDF
► (1/2) x 3 x 4 + 8 x 4 + (1/2) x 3 x 4 = 44 cm2
► (1/2) x 3 x 4 + 8 x 4 + (1/2) x 3 x 4 = 44 cm2
Most Upvoted Answer
ABCD is an isosceles trapezium such that AD || BC, AB = 5 cm, AD = 8 c...
Given: Isosceles trapezium ABCD, AD || BC, AB = 5 cm, AD = 8 cm, BC = 14 cm.
To find: Area of trapezium.
Approach: We can find the height of the trapezium using Pythagoras theorem and then use the formula for the area of trapezium to find the answer.
Solution:
- Draw a rough figure and mark the given values.
- Since AD || BC, we can draw a perpendicular from A to BC.
- Let E be the foot of the perpendicular from A to BC.
- We know that AE = 8 cm, AB = 5 cm, and BC = 14 cm.
- Using Pythagoras theorem, we can find the height of the trapezium.
- In right triangle ABE, BE2 + AE2 = AB2
- BE2 + 82 = 52
- BE2 = 25 - 64 = -39 (which is not possible)
- This means that the foot of the perpendicular E lies outside the line segment BC.
- We can extend BC to meet the perpendicular from A at F.
- Let FC = x cm.
- Then, BF = 14 - x cm.
- In right triangle AEF, AF2 + EF2 = AE2
- AF2 + x2 = 82
- AF2 = 64 - x2
- In right triangle BFC, BF2 + FC2 = BC2
- (14 - x)2 + x2 = 196
- 196 - 28x + 2x2 + x2 = 196
- 3x2 - 28x + 0 = 0
- Solving for x, we get x = 8/3 cm (approx)
- Therefore, BF = 14 - x = 38/3 cm (approx)
- Now, the height of the trapezium is EF = AF - AE = sqrt(64 - x2) - 8
- Plugging in the values, we get EF = 4/3 cm (approx)
- The area of the trapezium is given by (sum of parallel sides) x (height) / 2
- Area = (AB + DC) x EF / 2
- Area = (5 + 14) x (4/3) / 2
- Area = 44/3 cm2 (approx)
Therefore, the area of the trapezium is 44 cm2 (approx). Hence, option B is the correct answer.
To find: Area of trapezium.
Approach: We can find the height of the trapezium using Pythagoras theorem and then use the formula for the area of trapezium to find the answer.
Solution:
- Draw a rough figure and mark the given values.
- Since AD || BC, we can draw a perpendicular from A to BC.
- Let E be the foot of the perpendicular from A to BC.
- We know that AE = 8 cm, AB = 5 cm, and BC = 14 cm.
- Using Pythagoras theorem, we can find the height of the trapezium.
- In right triangle ABE, BE2 + AE2 = AB2
- BE2 + 82 = 52
- BE2 = 25 - 64 = -39 (which is not possible)
- This means that the foot of the perpendicular E lies outside the line segment BC.
- We can extend BC to meet the perpendicular from A at F.
- Let FC = x cm.
- Then, BF = 14 - x cm.
- In right triangle AEF, AF2 + EF2 = AE2
- AF2 + x2 = 82
- AF2 = 64 - x2
- In right triangle BFC, BF2 + FC2 = BC2
- (14 - x)2 + x2 = 196
- 196 - 28x + 2x2 + x2 = 196
- 3x2 - 28x + 0 = 0
- Solving for x, we get x = 8/3 cm (approx)
- Therefore, BF = 14 - x = 38/3 cm (approx)
- Now, the height of the trapezium is EF = AF - AE = sqrt(64 - x2) - 8
- Plugging in the values, we get EF = 4/3 cm (approx)
- The area of the trapezium is given by (sum of parallel sides) x (height) / 2
- Area = (AB + DC) x EF / 2
- Area = (5 + 14) x (4/3) / 2
- Area = 44/3 cm2 (approx)
Therefore, the area of the trapezium is 44 cm2 (approx). Hence, option B 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.
|
Explore Courses for CAT exam
|
|
Similar CAT Doubts
Top Courses for CATView all
ABCD is an isosceles trapezium such that AD || BC, AB = 5 cm, AD = 8 cm and BC = 14 cm. What is the area (in cm2) of trapezium?a)36b)44c)88d)144Correct answer is option 'B'. Can you explain this answer?
Question Description
ABCD is an isosceles trapezium such that AD || BC, AB = 5 cm, AD = 8 cm and BC = 14 cm. What is the area (in cm2) of trapezium?a)36b)44c)88d)144Correct answer is option 'B'. 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 ABCD is an isosceles trapezium such that AD || BC, AB = 5 cm, AD = 8 cm and BC = 14 cm. What is the area (in cm2) of trapezium?a)36b)44c)88d)144Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for ABCD is an isosceles trapezium such that AD || BC, AB = 5 cm, AD = 8 cm and BC = 14 cm. What is the area (in cm2) of trapezium?a)36b)44c)88d)144Correct answer is option 'B'. Can you explain this answer?.
ABCD is an isosceles trapezium such that AD || BC, AB = 5 cm, AD = 8 cm and BC = 14 cm. What is the area (in cm2) of trapezium?a)36b)44c)88d)144Correct answer is option 'B'. 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 ABCD is an isosceles trapezium such that AD || BC, AB = 5 cm, AD = 8 cm and BC = 14 cm. What is the area (in cm2) of trapezium?a)36b)44c)88d)144Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for ABCD is an isosceles trapezium such that AD || BC, AB = 5 cm, AD = 8 cm and BC = 14 cm. What is the area (in cm2) of trapezium?a)36b)44c)88d)144Correct answer is option 'B'. Can you explain this answer?.
Solutions for ABCD is an isosceles trapezium such that AD || BC, AB = 5 cm, AD = 8 cm and BC = 14 cm. What is the area (in cm2) of trapezium?a)36b)44c)88d)144Correct answer is option 'B'. 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 ABCD is an isosceles trapezium such that AD || BC, AB = 5 cm, AD = 8 cm and BC = 14 cm. What is the area (in cm2) of trapezium?a)36b)44c)88d)144Correct answer is option 'B'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
ABCD is an isosceles trapezium such that AD || BC, AB = 5 cm, AD = 8 cm and BC = 14 cm. What is the area (in cm2) of trapezium?a)36b)44c)88d)144Correct answer is option 'B'. Can you explain this answer?, a detailed solution for ABCD is an isosceles trapezium such that AD || BC, AB = 5 cm, AD = 8 cm and BC = 14 cm. What is the area (in cm2) of trapezium?a)36b)44c)88d)144Correct answer is option 'B'. Can you explain this answer? has been provided alongside types of ABCD is an isosceles trapezium such that AD || BC, AB = 5 cm, AD = 8 cm and BC = 14 cm. What is the area (in cm2) of trapezium?a)36b)44c)88d)144Correct answer is option 'B'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice ABCD is an isosceles trapezium such that AD || BC, AB = 5 cm, AD = 8 cm and BC = 14 cm. What is the area (in cm2) of trapezium?a)36b)44c)88d)144Correct answer is option 'B'. Can you explain this answer? tests, examples and also practice CAT tests.
|
|
Explore Courses for CAT exam
|
|
Suggested Free Tests
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