UPSC Exam > UPSC Questions > Find the area of the rhombus if its vertices ...
Start Learning for Free
Find the area of the rhombus if its vertices (3,0), (4,5), (-1, 4) and (-2,-4) are taken in order?
Most Upvoted Answer
Find the area of the rhombus if its vertices (3,0), (4,5), (-1, 4) and...
Finding the Area of the Rhombus
To find the area of the rhombus formed by the vertices (3,0), (4,5), (-1,4), and (-2,-4), we can use the formula for the area based on the coordinates of its vertices.
Step 1: Understand the Formula
The area (A) of a polygon defined by vertices can be calculated using the formula:
A = 1/2 * | Σ (x_i * y_(i+1) - y_i * x_(i+1)) |
where the points are taken in order and the last point connects back to the first.
Step 2: List the Coordinates
- (3,0)
- (4,5)
- (-1,4)
- (-2,-4)
Step 3: Apply the Formula
- Assign (x1, y1) = (3,0)
- Assign (x2, y2) = (4,5)
- Assign (x3, y3) = (-1,4)
- Assign (x4, y4) = (-2,-4)
Step 4: Calculate the Determinants
Using the formula, we will compute:
- x1*y2 + x2*y3 + x3*y4 + x4*y1
- y1*x2 + y2*x3 + y3*x4 + y4*x1
Calculating these values gives:
- (3*5) + (4*4) + (-1*-4) + (-2*0) = 15 + 16 + 4 + 0 = 35
- (0*4) + (5*-1) + (4*-2) + (-4*3) = 0 - 5 - 8 - 12 = -25
Step 5: Final Area Calculation
Now, calculate the area:
A = 1/2 * | 35 - (-25) | = 1/2 * | 35 + 25 | = 1/2 * 60 = 30 square units.
Conclusion
Thus, the area of the rhombus is 30 square units.
To find the area of the rhombus formed by the vertices (3,0), (4,5), (-1,4), and (-2,-4), we can use the formula for the area based on the coordinates of its vertices.
Step 1: Understand the Formula
The area (A) of a polygon defined by vertices can be calculated using the formula:
A = 1/2 * | Σ (x_i * y_(i+1) - y_i * x_(i+1)) |
where the points are taken in order and the last point connects back to the first.
Step 2: List the Coordinates
- (3,0)
- (4,5)
- (-1,4)
- (-2,-4)
Step 3: Apply the Formula
- Assign (x1, y1) = (3,0)
- Assign (x2, y2) = (4,5)
- Assign (x3, y3) = (-1,4)
- Assign (x4, y4) = (-2,-4)
Step 4: Calculate the Determinants
Using the formula, we will compute:
- x1*y2 + x2*y3 + x3*y4 + x4*y1
- y1*x2 + y2*x3 + y3*x4 + y4*x1
Calculating these values gives:
- (3*5) + (4*4) + (-1*-4) + (-2*0) = 15 + 16 + 4 + 0 = 35
- (0*4) + (5*-1) + (4*-2) + (-4*3) = 0 - 5 - 8 - 12 = -25
Step 5: Final Area Calculation
Now, calculate the area:
A = 1/2 * | 35 - (-25) | = 1/2 * | 35 + 25 | = 1/2 * 60 = 30 square units.
Conclusion
Thus, the area of the rhombus is 30 square units.
Attention UPSC Students!
To make sure you are not studying endlessly, EduRev has designed UPSC study material, with Structured Courses, Videos, & Test Series. Plus get personalized analysis, doubt solving and improvement plans to achieve a great score in UPSC.
|
Explore Courses for UPSC exam
|
|
Similar UPSC Doubts
Top Courses for UPSCView all
Find the area of the rhombus if its vertices (3,0), (4,5), (-1, 4) and (-2,-4) are taken in order?
Question Description
Find the area of the rhombus if its vertices (3,0), (4,5), (-1, 4) and (-2,-4) are taken in order? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about Find the area of the rhombus if its vertices (3,0), (4,5), (-1, 4) and (-2,-4) are taken in order? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Find the area of the rhombus if its vertices (3,0), (4,5), (-1, 4) and (-2,-4) are taken in order?.
Find the area of the rhombus if its vertices (3,0), (4,5), (-1, 4) and (-2,-4) are taken in order? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about Find the area of the rhombus if its vertices (3,0), (4,5), (-1, 4) and (-2,-4) are taken in order? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Find the area of the rhombus if its vertices (3,0), (4,5), (-1, 4) and (-2,-4) are taken in order?.
Solutions for Find the area of the rhombus if its vertices (3,0), (4,5), (-1, 4) and (-2,-4) are taken in order? in English & in Hindi are available as part of our courses for UPSC.
Download more important topics, notes, lectures and mock test series for UPSC Exam by signing up for free.
Here you can find the meaning of Find the area of the rhombus if its vertices (3,0), (4,5), (-1, 4) and (-2,-4) are taken in order? defined & explained in the simplest way possible. Besides giving the explanation of
Find the area of the rhombus if its vertices (3,0), (4,5), (-1, 4) and (-2,-4) are taken in order?, a detailed solution for Find the area of the rhombus if its vertices (3,0), (4,5), (-1, 4) and (-2,-4) are taken in order? has been provided alongside types of Find the area of the rhombus if its vertices (3,0), (4,5), (-1, 4) and (-2,-4) are taken in order? theory, EduRev gives you an
ample number of questions to practice Find the area of the rhombus if its vertices (3,0), (4,5), (-1, 4) and (-2,-4) are taken in order? tests, examples and also practice UPSC tests.
|
|
Explore Courses for UPSC 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
|
Follow Us
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup