# 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 = $\Pi&space;r^{2}\frac{\Theta&space;}{360}$

$=\frac{22}{7}\times&space;14\times&space;14\times&space;\frac{45}{360}$

=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

$\Pi&space;r^{2}=\frac{22}{7}\times&space;\frac{7}{2}\times&space;\frac{7}{2}=38.5$

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 = $\frac{\sqrt{3}}{4}a^{2}=12\sqrt{3}$