ABCD is a given rectangle with length as 80 cm and breadth as 60 cm. P, Q, R, S are the mid points of sides AB, BC, CD, DA respectively. - Mathematics

Advertisements
Advertisements
Sum

ABCD is a given rectangle with length as 80 cm and breadth as 60 cm. P, Q, R, S are the midpoints of sides AB, BC, CD, DA respectively. A circular rangoli of radius 10 cm is drawn at the centre as shown in the given figure. Find the area of shaded portion.

Advertisements

Solution

Here, AP = `1/2` AB = `1/2 xx 80` = 40 cm

Also, AS = `1/2` AD = `1/2 xx 60` = 30 cm

Area of ΔAPS = `1/2` × AP × AS = `1/2` × 40 × 60 = 600 cm2

Area of portion PQRS = Area of rectangle ABCD – 4 × Area of ΔAPS

= 80 × 60 – 4 × 600 

= 4800 – 2400

= 2400 cm 

Area of circular rangoli = π × (10)2  ......[∵ Radius of circle = 10 cm]

= `22/7 xx 100`

= 314 cm2  

∴ Area of shaded region = 2400 – 314 = 2086 cm2

  Is there an error in this question or solution?
Chapter 9: Perimeter and Area - Exercise [Page 297]

APPEARS IN

NCERT Exemplar Mathematics Class 7
Chapter 9 Perimeter and Area
Exercise | Q 127. | Page 297

Video TutorialsVIEW ALL [1]

RELATED QUESTIONS

The radius of a circle is 7 cm. find the circumference of the circle.


An elastic belt is placed round the rim of a pulley of radius 5 cm. One point on the belt is pulled directly away from the centre O of the pulley until it is at P, 10 cm from O. Find the length
of the belt that is in contact with the rim of the pulley. Also, find the shaded area.


Find the circumference of the circle with the following radius (Take `pi = 22/7`) 

28 mm


If the circumference of a circular sheet is 154 m, find its radius. Also find the area of

the sheet. (Take `pi = 22/7`)


A gardener wants to fence a circular garden of diameter 21 m. Find the length of the rope he needs to purchase, if he makes 2 rounds of fence. Also find the costs of the rope, if it cost ₹ 4 per meter (Take `pi = 22/7`)


Find the circumference of the inner and the outer circles, shown in the adjoining figure? (Take π = 3.14)


A doorway is decorated as shown in the figure. There are four semi-circles. BC, the diameter of the larger semi-circle is of length 84 cm. Centres of the three equal semicircles lie on BC. ABC is an isosceles triangle with AB = AC. If BO = OC, find the area of the shaded region. (Take `pi = 22/7`)


A car travels 1 km distance in which each wheel makes 450 complete revolutions. Find the radius of wheel.


In circle of radius 6cm, chord of length 10 cm makes an angle of 110° at the centre of circle find Circumference of the circle


In the given figure, the radius of the circle is 7 cm and m ( arc MBN) = 60°,
find  A(O - MCN). 

In the given figure, O is the centre of the sector. \[\angle\]ROQ =  \[\angle\]MON = 60° . OR = 7 cm, and   OM = 21 cm. Find the lengths of  arc RXQ and arc MYN. (\[\pi = \frac{22}{7}\]) 


In the given figure, if A(P-ABC) = 154 cm2  radius of the circle is 14 cm, find

(1) `∠APC` 

(2) l ( arc ABC) .


The radius of a sector of a circle is 7 cm. If the measure of the arc of the sector is 210°,  find the area of the sector in case.


The radius of a sector of a circle is 7 cm. If the measure of the arc of the sector is - three right angles; find the area of the sector in case.


In the given figure,

\[\square\] PQRS is a rectangle. If PQ = 14 cm, QR = 21 cm, find the areas of the parts x, y, and z.  


Choose the correct alternative answer for the following question.
The ratio of circumference and area of a circle is 2:7. Find its circumference.

Choose the correct alternative answer for the following question.
If measure of an arc of a circle is 160° and its length is 44 cm, find the circumference of the circle.
 

Choose the correct alternative answer for the following question.

 Find the curved surface area of a cone of radius 7 cm and height 24 cm.

Choose the correct alternative answer for the following question.

A cone was melted and cast into a cylinder of the same radius as that of the base of the cone. If the height of the cylinder is 5 cm, find the height of the cone.

 

Choose the correct alternative answer for the following question.

Find the side of a cube of volume 1 m3.

Diagonal of a square is 20 cm. Find the length and perimeter of the square.


A wire when bent in the form of an equilateral triangle encloses an area of `121sqrt(3)  "cm"^2`. The same wire is bent to form a circle. Find the area enclosed by the circle.


A chord of a circle of radius 30 cm makes an angle of 60° at the centre of the circle. Find the areas of the minor major segments.


The area of a circle inscribed in an equilateral triangle is 154 cm2. Find the perimeter of the triangle.


If the perimeter of a square is equal to the circumference of a circle then the ratio of their areas is


Radii of the circles are given below, find their areas.
(1) 28 cm
(2) 10.5 cm
(3) 17.5 cm


Areas of some circles are given below find their diameters.
(1) 176 sq cm
(2) 394.24 sq cm
(3) 12474 sq cm


Diameter of the circular garden is 42 m. There is a 3.5 m wide road around the garden. Find the area of the road.


Find the area of the circle if its circumfence is 88 cm.


Find the area and perimeter of the circle with the following :

 Diameter = 77 cm 


Find the area and perimeter of the circle with the following:

Diameter= 35 cm 


The diameter of a cycle wheel is `4 5/11` cm. How many revolution will it make in moving 6.3 km ?


Find the area enclosed between two concentric circles, if their radii are 6 cm and 13 cm respectively. 


The area between the circumferences of two concentric circles is 2464 cm2. If the inner circle has circumference of 132 cm, calculate the radius of outer circle.


A conical tent with a capacity of 600 m3 stands on a circular base of area 160 m2 Find in m2 the area of the canvas. 


Find the area and perimeter of the following semi-circle :

Diameter= 5.6 cm 


The sum of diameter of two circles is 112 cm and the sum of their areas is 5236 cm2 Find the radii of the two circles. 


Sand from a cylindrical bucket 32 cm in height and 18 cm in radius is poured onto the ground making a conical heap 24 cm high. Find the radius of the conical heap. 


Find the area and perimeter of the following sector :

Radius= 4.2 cm, angle at the centre is 60 ° 


The speed of the car is 66 km/hour. If each wheel of the car is 140 cm in diameter, find the number of revolutions made by each wheel per minute.


A cart wheel makes 9 revolutions per second. If the diameter of the wheel is 42 cm, find its speed in km/hr. 


Find the volume and the surface area of the spheres in the following :

Radius= 2.1 cm 


Find the diameter of the sphere for the following : 

Surface Area = `576pi`cm2


A metal wire, when bent in the form of an equilateral triangle of largest area, encloses an area of 484 `sqrt3` cm2. If the same wire is bent into the form of a circle of largest area, find the area of this circle.


The radii of two circles are 48 cm and 13 cm. Find the area of the circle which has its circumference equal to the difference of the circumferences of the given two circles.


The shaded portion of the figure, given alongside, shows two concentric circles. If the circumference of the two circles is 396 cm and 374 cm, find the area of the shaded portion.


Draw the circumcircle of Δ PMT in which PM = 5.4, P = 60°, M = 70°.


The radius of a circle is 21 cm. Find the circumference (Take π = `3 1/7`).


The circumference of a circle is 440 cm. Find its radius and diameter. (Take π = `22/7`)


The radius of two circles are 20 cm and 13 cm. Find the difference between their circumferences. (Take π =`22/7`)


The perimeter of a square and the circumference of a circle are equal. If the length of each side of the square is 22 cm, find:
(i) perimeter of the square.
(ii) circumference of the circle.
(iii) radius of the circle.


Find the radius of the circle whose circumference is equal to the sum of the circumferences of the circles having radius 15 cm and 8 cm.


Find the diameter of a circle whose circumference is equal to the sum of circumference of circles with radius 10 cm, 12 cm, and 18 cm.


The radius of two circles are in the ratio 3 : 5, find the ratio between their circumferences.


Each side of a square is 44 cm. Find its perimeter. If this perimeter is equal to the circumference of a circle, find the radius of the circle.


A circular racing track has inner circumference 528 m and outer circumference 616 m. Find the width of the track.


The inner circumference of a circular track is 264 m and the width of the track is 7 m. Find:
(i) the radius of the inner track.
(ii) the radius of the outer circumference.
(iii) the length of the outer circumference.
(iv) the cost of fencing the outer circumference at the rate of ₹50 per m.


The center O of a circle of a radius 1.3 cm is at a distance of 3.8 cm from a given straight line AB. Draw a circle to touch the given straight line AB at a point P so that OP = 4.7 cm and to touch the given circle externally.


In the adjoining figure, the radius is 3.5 cm. Find:
(i) The area of the quarter of the circle correct to one decimal place.
(ii) The perimeter of the quarter of the circle correct to one decimal place. ( Take π = `22/7`)


Complete the table below.

Radius (r)  Diameter (d) Circumference (c)
7 cm ______ _______

Complete the table below.

Radius (r)  Diameter (d) Circumference (c)
_______ _________ 616 cm

Complete the table below.

Radius (r)  Diameter (d) Circumference (c)
_______ _________ 72.6 cm

If the circumference of a circle is 176 cm, find its radius.


The radius of a circular garden is 56 m. What would it cost to put a 4-round fence around this garden at a rate of 40 rupees per metre?


The wheel of a bullock cart has a diameter of 1.4 m. How many rotations will the wheel complete as the cart travels 1.1 km?


The diameter of a circle is 5.6 cm. Find its circumference.


The diameter of the wheel of a cart is 1.05 m. How much distance will the cart cover in 1000 rotations of the wheel?


Find the area and perimeter of the following semicircles: Diameter = 7cm


Find the area of a circular field that has a circumference of 396m.


The circumference of a circle is numerically equal to its area. Find the area and circumference of the circle.


The diameter of two circles are 28 cm and 24 cm. Find the circumference of the circle having its area equal to sum of the areas of the two circles.


The wheel of a car makes 10 revolutions per second. If its diameter is 70cm, find the speed of the car in km per hr.


A wire when bent in the form of a square encloses an area of 484cm2. If the same wire is bent into the form of a circle, find the area of the circle.


The cost of fencing a circular field at the rate of Rs.250 per metre is Rs.55000. The field is to be ploughing at the rate of Rs.15 per m2. Find the cost of ploughing the field.


The radius of a circular plot is 7.7 metres. How much will it cost to fence the plot with 3 rounds of wire at the rate of 50 rupees per metre?


The radius of the wheel of a bus is 0.7 m. How many rotations will a wheel complete while traveling a distance of 22 km?


Diameters of different circles are given below. Find their circumference (Take π = `22/7`)

d = 56 m


Find the circumference of the circles whose radii are given below.

49 cm


The diameter of a circular well is 4.2 m. What is its circumference?


The diameter of the bullock cart wheel is 1.4 m. Find the distance covered by it in 150 rotations?


A ground is in the form of a circle whose diameter is 350 m. An athlete makes 4 revolutions. Find the distance covered by the athlete


A wire of length 1320 cm is made into circular frames of radius 7 cm each. How many frames can be made?


A Rose garden is in the form of circle of radius 63 m. The gardener wants to fence it at the rate of ₹ 150 per metre. Find the cost of fencing?


If the circumference of a circle is 82π, then the value of ‘r’ is


A wheel of a car covers a distance of 3520 cm in 20 rotations. Find the radius of the wheel?


The cost of decorating the circumference of a circular lawn of a house at the rate of ₹ 55 per metre is ₹ 16940. What is the radius of the lawn?


In a circle of diameter 42 cm, if an arc subtends an angle of 60° at the centre, where `pi = 22/7` then length of an arc is ____________.


The numerical value of the area of a circle is greater than the numerical value of its circumference. Is this statement true? Why?


In reference to a circle the value of π is equal to ______.


The area of a square is 100 cm2. The circumference (in cm) of the largest circle cut of it is ______.


A circle with radius 16 cm is cut into four equal parts and rearranged to form another shape as shown in the below figure:


Does the perimeter change? If it does change, by how much does it increase or decrease?


Find the total cost of wooden fencing around a circular garden of diameter 28 m, if 1 m of fencing costs ₹ 300.


The moon is about 384000 km from earth and its path around the earth is nearly circular. Find the length of path described by moon in one complete revolution. (Take π = 3.14)


A photograph of Billiard/Snooker table has dimensions as `1/10`th of its actual size as shown in the given figure:


The portion excluding six holes each of diameter 0.5 cm needs to be polished at rate of ₹ 200 per m2. Find the cost of polishing.


Share
Notifications



      Forgot password?
Use app×