Mensuration Part 11

Problem 1: Radius of a circle is 14cm. and the angle at the center formed by a sector is 45 degrees. Find the area of the sector?

Solution:

Area of a sector = \Pi r^{2}\frac{\Theta }{360}

=\frac{22}{7}\times 14\times 14\times \frac{45}{360}

=77

Problem 2: A rectangular sheet of 30 m × 20 m dimension is cut from its every corner as a quadrant of radius 3.5m. Find the area of remaining portion?

Solution:

4 sectors = 1 circle

Area of rectangle = 30*20=600

\Pi r^{2}=\frac{22}{7}\times \frac{7}{2}\times \frac{7}{2}=38.5

600-38.5= 561.5

Problem 3: Smaller diagonal of a rhombus is equal to the length of its sides. If the length of each side is 4 cm, then what is the area (in cm2) of an equilateral triangle with side equal to the bigger diagonal of the rhombus?

Solution:
Area of equilateral triangle = \frac{\sqrt{3}}{4}a^{2}=12\sqrt{3}

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