 Hello and welcome to the session. I am Deepika here. Let's discuss the question which says, in given figure, a round table cover has 6 equal designs. If the radius of the cover is 28 centimeter, find the cost of making the designs at the rate of Rs 0.35 per centimeter square. Use root 3 is equal to 1.7. Now this problem is based on the area of a segment of a circle and we know that area of a segment of a circle is equal to area of the corresponding sector minus area of the corresponding triangle. So this is a key idea behind our question. We will take the help of this key idea to solve the above question. So let's start the solution. Now in this question a round table cover has 6 equal designs that is the circle is divided it into 6 equal parts. Now in this question a round table cover has 6 equal designs that is the circle is divided into 6 equal parts. Let us join these parts. Now we have to find the area of these 6 segments. For this first we will find the area of these 6 sectors. Now the area of 6 sectors is equal to the area of circle because the circle is divided into 6 equal parts. Now given radius of the circle is equal to 28 centimeter. Therefore area of circle is equal to pi r square. Take pi is equal to 22 over 7 into 28 into 28 centimeter square and on cancellation we have this is equal to 2464 centimeter square. Since the circle is divided into 6 equal parts, therefore the angle 360 degrees is also divided into 6 equal parts. Thus the angle of each sector is equal to 360 degree upon 6. This is equal to 60 degree. Now we have found the area of 6 sectors. Now we will find the area of these 6 triangles. Let us take one triangle as triangle a o b at the center is 60 degree. So in triangle is equal to 60 degree o a is equal to o b is equal to 28 centimeter radii of the circle a b is equal to angle o b a because this is an property of isocialist triangle that equal sides have equal angles opposite to them. So in triangle we have angle a o b plus angle o a b plus angle o b a is equal to 180 degree angle some property of a triangle. Therefore angle o a b plus angle o b a is equal to 180 degree minus angle a o b and this is equal to 180 degree minus 60 degree is equal to 120 degree. Hence angle o a b is equal to angle o b a is equal to 60 degree like this 120 over 2 is equal to 60 degree. Thus triangle a o b is an equilateral triangle whose each side is 28 centimeter. Now we know the formula for the area of an equilateral triangle is equal to root 3 by 4 into side square and this is equal to root 3 upon 4 into 28 into 28 centimeter square and this is equal to 28 into 7 into root 3 centimeter square and this is equal to 196 root 3 centimeter square. Now here we have 6 triangles so the total area of 6 triangles is equal to 6 into 196 root 3 centimeter square and this is equal to 1176 root 3 centimeter square and this is again equal to 1176 into 1.7 centimeter square because root 3 is equal to 1.7 given and this is equal to 199.2 centimeter square. Thus the total area of the designs is equal to the circle minus area of 6 triangles. Now area of the circle is 2464 centimeter square minus 19.2 centimeter square and this is equal to 464 centimeter square meter square of design is equal to rupees 0.35 therefore the cost of 464.8 centimeter square of design is equal to rupees 0.35 into 464.8 and this is equal to 162 question is rupees hope the solution is clear to you buy and take care