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Find the area of the rhombus if its vertices (3,0), (4,5), (-1, 4) and (-2,-4) are taken in order?
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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.
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Find the area of the rhombus if its vertices (3,0), (4,5), (-1, 4) and (-2,-4) are taken in order?
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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?.
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