Area Related to...

In the given figure, a quadrant of a circle with centre S, is occupied by a square PQRS. The area of the shaded portion will be what fraction of thearea of the circle, if the side of the square is 14 cm?

A circular field of area 5544 m², has a fence around it. If the same fence is to be used around a new rectangular field of length 115 m and area 9775 m², then how much more fence is required? [Take π =]

In a quadrilateral park, two opposite sides having length 42 m and 48 m, are parallel and the distance between them is 18 m. If on all the corners of the park, arcs of the same radius, i.e. 3.5 m, are cut and areas enclosed within the arcs are kept without grass to make refreshment corners in the park, then what will be the area of the park which is covered by grass? [Take π =]

Find the sum of the area of a circle and that of a square, if the circumference of the circle is 88 m and the side of the square is twice the radius of the circle.

A regular hexagonal ground is inscribed in a circular field which has a radius of 24 m. What is the area of the field left unused around the hexagonal ground in that circular field?

In the figure given below, ABCD is a square with each side measuring 7 cm and a circle is inscribed in the square.



What is the total area of the shaded region?

The sum of the area of a circular park and the total area including the jogging path around that is 2550.465 m². Also, the area of the park including the jogging path and the area of the park are in the ratio 5 : 4. What is the width of the jogging path? [Take π = 3.14]

What will be the area of the minor sector, if a chord of a circle of radius 63 cm subtends an angle of 120° at the centre of the circle? [Take π =]

In the circle given below, find the area of the shaded region, if the radius of the circle is 14 cm.

Calculate the area of the remaining portion, after cutting two quadrants (quarter circles), each of radius 13 cm, from the two corners of a rectangle measuring 35 cm by 25 cm.

Find the length of chord AB of a circle of radius 5 cm if point A meets the largest chord of the circle on its circumference at points B and C respectively and AC = 6 cm.

A square circumscribes a circle. Find the area enclosed between the square and the circle, if radius of the circle is 10 cm.

In the given parallelogram PQRS, if the area of the shaded part of the circle with centre S and radius 14 cm is 462 cm², then
(Take = 22/7)

In the given figure, a circle is drawn with B as the centre and AC as the diameter; two semicircles are drawn with AB and BC as diameters. If the perimeter of the shaded portion is 280 cm, what will be the radius of the semicircle whose diameter is AB?

A circular park has a concrete road 7 m wide build around its perimeter. If its inner perimeter is 22 m, what will be the ratio of the inner diameter to the outer diameter?

James is driving his car in the rain. He uses its wipers to clean its glass. If the length of its each blade of the wiper is 21.5 cm and they are sweeping through an angle of 105°, then what will be the total area cleaned at each sweep of the blades?

Milli has a square cardboard whose area is 196 cm². She wants to cut a semicircle from this square cardboard. If she manages to cut a semicircle along one of the sides of the square cardboard, then which of the following represents the radius of the semicircle?

A and B have two threads and they used these threads to prepare circles. A prepares a circle whose radius is 6.7 cm and B prepares a circle whose radius is 18.4 cm. They decide to prepare a bigger circle using these two threads. What is the area of the new circle?

Maddison is asked to find the length of the arc of that sector of a circle whose area is 9π cm². It is also given that the diameter of this circle is 18 cm. According to this information, which of the following represents the value of the length of the arc?

The area of the shaded part in the given figure is 40 cm². Which of the following represents the area of the un-shaded part, which is ΔAOB?

A train is travelling at a speed of 108 km per hour. If the area of a wheel of the train is 18,634 cm², then how many complete revolutions does each wheel make in 13 minutes?

Match the shaded regions given in the figures below with their areas.

A circle has a diameter of 64 cm. An equilateral triangle with the largest possible side length is drawn inside the circle and the corners of the triangle are touching the circle. If Priya decides to cut the triangle out, then what will be the area of the remaining part?

P is trying to make a drawing. He has a rectangle ABCD with dimensions 6 cm × 4 cm. He joined a semicircle whose diameter is the same as the length of this rectangle. What is the area of this drawing?

Which of the following are the correct answers according to the given statements?

(I) P has a circle whose circumference is 44.87 cm. He wants to find out the area of a quadrant of this circle. What will be the area of the quadrant of this circle?
(II) A has a square inside a circle whose diameter is 14.8 cm. If the square has each side of 12.8 cm, then what will be the area of the shaded part in the given diagram?

(III) If the perimeter of a circle is c, the which of the expressions represents the radius of the circle?