Question : A kite in the shape of a square with a diagonal 32 cm attached to an equilateral triangle of the base 8 cm. Approximately how much paper has been used to make it?(Use $\sqrt3$ = 1.732)
Option 1: 539.712 cm2
Option 2: 538.721 cm2
Option 3: 540.712 cm2
Option 4: 539.217 cm2
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Correct Answer: 539.712 cm2
Solution :
Area of the square = $\frac{1}{2}$ × (diagonal)2 = $\frac{1}{2}×32^2$ = $512$ cm2 Area of the equilateral triangle = $\frac{\sqrt3}{4}$×(side)2 = $\frac{\sqrt3}{4}×8^2$ = $16\sqrt3$ cm2 Total area = $512$ + $16\sqrt3$ = 512 + 27.712 = 539.712 cm2 Hence, the correct answer is 539.712 cm2.
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Question : The median of an equilateral triangle is $6\sqrt3$ cm. The area (in cm2) of the triangle is:
Option 1: $72$
Option 2: $108$
Option 3: $72\sqrt3$
Option 4: $36\sqrt3$
Question : If the altitude of a right prism is 10 cm and its base is an equilateral triangle of side 12 cm, then its total surface area (in cm2) is:
Option 1: $(5+3\sqrt3)$
Option 2: $36\sqrt3$
Option 3: $360$
Option 4: $72(5+\sqrt3)$
Question : A right pyramid stands on a square base of diagonal $10\sqrt2$ cm. If the height of the pyramid is 12 cm, the area (in cm2) of its slant surface is:
Option 1: 520 cm2
Option 2: 420 cm2
Option 3: 360 cm2
Option 4: 260 cm2
Question : A right prism stands on a base 6 cm equilateral triangle and its volume is $81\sqrt3$ cm3. The height (in cm) of the prism is:
Option 1: 9
Option 2: 10
Option 3: 12
Option 4: 15
Question : The base of a right pyramid is an equilateral triangle of side $10\sqrt3$ cm. If the total surface area of the pyramid is $270\sqrt3$ sq. cm. its height is:
Option 1: $12\sqrt3$ cm
Option 2: $10$ cm
Option 3: $10\sqrt3$ cm
Option 4: $12$ cm
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