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What will be the area of a rhombus, whose one side is 20 cm and one diagonal is 24 cm?
- a)240 cm2
- b)480 cm2
- c)384 cm2
- d)386 cm2
Correct answer is option 'C'. Can you explain this answer?
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Verified Answer
What will be the area of a rhombus, whose one side is 20 cm and one d...
Let length of another =diagnol =2x
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Diagnols of a rhombus intersect at right angles, so buy using pythagorus theorem,
X2 + 122 = 202
Therefore x =16, so diagonal = 2 x 16 = 32
Area of rhombus
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What will be the area of a rhombus, whose one side is 20 cm and one d...
Understanding the Rhombus
A rhombus is a type of polygon that is a quadrilateral with all four sides of equal length. The area of a rhombus can be calculated using the lengths of its diagonals or its base and height. In this case, we are given one side and one diagonal.
Given Data
- Side of the rhombus (a) = 20 cm
- One diagonal (d1) = 24 cm
Finding the Other Diagonal
To find the area, we first need to calculate the length of the other diagonal (d2) using the relationship between the sides and the diagonals in a rhombus. The diagonals bisect each other at right angles.
Using the Pythagorean theorem in one of the triangles formed by the diagonals, we have:
- Half of diagonal 1 (d1/2) = 24/2 = 12 cm
- Half of diagonal 2 (d2/2) = x (unknown)
- Side of rhombus (a) = 20 cm
According to the Pythagorean theorem:
20^2 = 12^2 + x^2
Simplifying, we find:
400 = 144 + x^2
Thus, x^2 = 256, and x = 16 cm. Therefore, d2 = 2 * 16 = 32 cm.
Calculating the Area
The area (A) of a rhombus can be calculated using the formula:
A = (d1 * d2) / 2
Substituting the known values:
A = (24 * 32) / 2
A = 768 / 2
A = 384 cm²
Conclusion
Therefore, the area of the rhombus is 384 cm², confirming that the correct answer is option 'C'.
A rhombus is a type of polygon that is a quadrilateral with all four sides of equal length. The area of a rhombus can be calculated using the lengths of its diagonals or its base and height. In this case, we are given one side and one diagonal.
Given Data
- Side of the rhombus (a) = 20 cm
- One diagonal (d1) = 24 cm
Finding the Other Diagonal
To find the area, we first need to calculate the length of the other diagonal (d2) using the relationship between the sides and the diagonals in a rhombus. The diagonals bisect each other at right angles.
Using the Pythagorean theorem in one of the triangles formed by the diagonals, we have:
- Half of diagonal 1 (d1/2) = 24/2 = 12 cm
- Half of diagonal 2 (d2/2) = x (unknown)
- Side of rhombus (a) = 20 cm
According to the Pythagorean theorem:
20^2 = 12^2 + x^2
Simplifying, we find:
400 = 144 + x^2
Thus, x^2 = 256, and x = 16 cm. Therefore, d2 = 2 * 16 = 32 cm.
Calculating the Area
The area (A) of a rhombus can be calculated using the formula:
A = (d1 * d2) / 2
Substituting the known values:
A = (24 * 32) / 2
A = 768 / 2
A = 384 cm²
Conclusion
Therefore, the area of the rhombus is 384 cm², confirming that the correct answer is option 'C'.
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What will be the area of a rhombus, whose one side is 20 cm and one diagonal is 24 cm?a)240 cm2b)480 cm2c)384 cm2d)386 cm2Correct answer is option 'C'. Can you explain this answer?
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