Question : Find the area of a rhombus if the perimeter of the rhombus is 52 cm, and one of its diagonals is 10 cm long.
Option 1: 120 cm2
Option 2: 164 cm2
Option 3: 160 cm2
Option 4: 144 cm2
Correct Answer: 120 cm2
Solution : The perimeter of a rhombus = 52 cm One diagonal = 10 cm Let the length of the other diagonal be $x$ cm. Perimeter = 4 × side 52 = 4 × side Side = $\frac{52}{4} = 13$ The diagonals of a rhombus bisect each other at right angles. Length of other diagonal = $2\sqrt{13^2-(\frac{10}{2})^2}$ $x = 2\sqrt{169-25}$ ⇒ $x = 2 × \sqrt{144}$ ⇒ $x = 2 × 12 = 24$ cm ⇒ Area of rhombus = $\frac{1}{2}$ × product of diagonals = $\frac{1}{2}×10×24$ = 5 × 24 = 120 cm2 Hence, the correct answer is 120 cm2.
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Question : One side of a rhombus is 13 cm and one of its diagonals is 10 cm. What is the area of the rhombus (in cm2)?
Option 1: 60
Option 2: 90
Option 3: 30
Option 4: 120
Question : If the perimeter of a rhombus is 40 cm and one of its diagonals is 16 cm, what is the area (in cm2) of the rhombus?
Option 1: 72
Option 2: 48
Option 3: 96
Option 4: 192
Question : One side of a rhombus is 13 cm and one of its diagonals is 24 cm. What is the area (in cm2) of the rhombus?
Option 1: 120
Option 4: 60
Question : If the perimeter of a rhombus is 80 cm and one of its diagonals is 24 cm, then what is the area (in cm2) of the rhombus?
Option 1: 218
Option 2: 192
Option 3: 384
Option 4: 768
Question : The area of a rhombus having one side measuring 17 cm and one diagonal measuring 16 cm is:
Option 1: 280 cm2
Option 2: 180 cm2
Option 3: 240 cm2
Option 4: 210 cm2
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