Manipur Board Solutions for Chapter: Mensuration, Exercise 3: EXERCISE 12.3

From an equilateral triangle of sides $14 \mathrm{cm}$, a sector of radius $7 \mathrm{cm}$ with centre at a vertex and enclosed by two sides, is cut off. Find the area of the remaining portion. (take $\sqrt{3}=1.73$)

$ABC$ is an isosceles right angled triangle, right angled at $A$ where $AB=AC=8 \mathrm{cm}$. A sector of radius $3.5 \mathrm{cm}$ with centre $A$ enclosed by $AB, AC$ is cut off from the triangle. Find the area of the remaining portion.

$BC$ is the arc of a quadrant of a circle of radius $8 \mathrm{cm}$. A semi-circle is described on the chord $BC$ on the side opposite to the centre of the quadrant. Find the area enclosed between arc $BC$ and the semi circle.

In a $400 \mathrm{m}$ track the length of each of the straight portions is $90 \mathrm{m}$ and the diameter of each of the inner semi-circular ends is $70 \mathrm{m}$. If the uniform width of the track is $7 \mathrm{m}$, find the cost of turfing the track at the rate of $₹250$ per square metre.

Two flower beds are in the form of segments (minor) of the circle circumscribing a square field of side $42 \mathrm{m}$, with two opposite sides of square as the corresponding chords. Find the cost of planting flowers at the rate of $₹200$ per square metre.

On a rectangular window of dimension, $84 \mathrm{cm}\times 56 \mathrm{cm}$, twenty four nonoverlapping circular designs each of radius $7 \mathrm{cm}$ are made at the rate of $₹25 \mathrm{per} 20 {\mathrm{cm}}^2$. Find the cost of making the designs. 

In a round table of diameter $112 \mathrm{cm}$, there is a portion in the form of a regular hexagon inscribed in it. Designs are made on the remaining portion of the table top at the rate of $₹8 \mathrm{per} 15 {\mathrm{cm}}^2$. Find the cost of designing (use $\sqrt{3}=1.73$).​

Find the area of the shaded region in the given figure, having given that $\mathrm{OA}=\mathrm{OB}=28 \mathrm{cm}$