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If A(2, -1), B(3, 4) C(-2, 3) and D(-3, -2) be four points in a plane so that ABCD is a rhombus but not a square. Find the area of rhombus?
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If A(2, -1), B(3, 4) C(-2, 3) and D(-3, -2) be four points in a plane ...
Introduction:
To find the area of a rhombus, we need to know the length of its diagonals. Diagonals of a rhombus bisect each other at right angles.
Step 1: Find the length of diagonals
Using the distance formula, we can find the length of diagonals AC and BD.
AC = √[(3 - (-2))^2 + (4 - 3)^2] = √(5^2 + 1^2) = √26
BD = √[(2 - (-3))^2 + (-1 - (-2))^2] = √(5^2 + 1^2) = √26
Step 2: Calculate the area of the rhombus
Area of a rhombus = (diagonal 1 * diagonal 2)/2
Area of ABCD = (AC * BD)/2 = (√26 * √26)/2 = 13
Conclusion:
The area of the given rhombus ABCD is 13 square units.
To find the area of a rhombus, we need to know the length of its diagonals. Diagonals of a rhombus bisect each other at right angles.
Step 1: Find the length of diagonals
Using the distance formula, we can find the length of diagonals AC and BD.
AC = √[(3 - (-2))^2 + (4 - 3)^2] = √(5^2 + 1^2) = √26
BD = √[(2 - (-3))^2 + (-1 - (-2))^2] = √(5^2 + 1^2) = √26
Step 2: Calculate the area of the rhombus
Area of a rhombus = (diagonal 1 * diagonal 2)/2
Area of ABCD = (AC * BD)/2 = (√26 * √26)/2 = 13
Conclusion:
The area of the given rhombus ABCD is 13 square units.
Community Answer
If A(2, -1), B(3, 4) C(-2, 3) and D(-3, -2) be four points in a plane ...
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If A(2, -1), B(3, 4) C(-2, 3) and D(-3, -2) be four points in a plane so that ABCD is a rhombus but not a square. Find the area of rhombus?
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