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
Correct Answer: 240 cm2
Solution : Length of side = 17 cm Length of a diagonal = 16 cm The two diagonals bisect each other at 90$^\circ$ in a rhombus. Area of rhombus = ($\frac{1}{2}$) × Product of the two diagonals Let AC = 16 cm and BD = x cm If the two diagonals of rhombus ABCD intersect at O then, $AO^2 + BO^2 = AB^2$ ⇒ $\left(\frac{16}{2}\right)^2 + \left(\frac{x}{2}\right)^2 = 17^2$ ⇒ $64 + \left(\frac{x^2}{4}\right) = 289$ ⇒ $\left(\frac{x^2}{4}\right) = 225$ ⇒ $x^2= 900$ $\therefore x = 30$ cm Area of rhombus = ($\frac{1}{2}$) × 16 × 30 = 8 × 30 = 240 cm2 Hence, the correct answer is 240 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 : 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 : 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
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 : A right square pyramid having a lateral surface area is 624 cm2. If the length of the diagonal of the square is $24 \sqrt{2}$, then the volume of the pyramid is:
Option 1: 1150 cm3
Option 2: 780 cm3
Option 3: 1083 cm3
Option 4: 960 cm3
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