NCERT Solution For Class 7 Maths – Perimeter And Area

NCERT Solutions is known as an extremely helpful resource for preparing for the exam. Takshila Learning provides its learners with access to a wealth of NCERT problems and their solutions. CBSE Class 7 Science NCERT Solutions are built by subject matter experts, so be sure to train learners for a good grade. The questions set out in the NCERT

NCERT Solution For Class 7 Maths – Integers provides us with all-inclusive information on all concepts. As students would have to learn the basics about the subject in class 7, this curriculum for class 7 is comprehensive study material, which explains the concepts in a great way.

Questions Covered : 

Question 1 : The length and the breadth of a rectangular piece of land are 500 m and 300 m respectively. Find
(i) its area
(ii)the cost of the land, if 1 m2 of the land costs Rs 10,000.

Question 2 : Find the area of a square park whose perimeter is 320 m.

Question 3 : Find the breadth of a rectangular plot of land, if its area is 440 m2 and the length is 22 m. Also find its perimeter.

Question 4 : The perimeter of a rectangular sheet is 100 cm. If the length is 35 cm, find its breadth. Also find the area.

Question 5 : The area of a square park is the same as of a rectangular park. If the side of the square park is 60 m and the length of the rectangular park is 90 m, find the breadth of the rectangular park.

Question 6 : A wire is in the shape of a rectangle. Its length is 40 cm and breadth is 22 cm. If the same wire is rebent in the shape of a square, what will be the measure of each side. Also find which shape encloses more area?

Question 7 : The perimeter of a rectangle is 130 cm. If the breadth of the rectangle is 30 cm, find its length. Also find the area of the rectangle.

Question 8 : A door of length 2 m and breadth 1 m is fitted in a wall. The length of the wall is 4.5 m and the breadth is 3.6 m (see the given figure). Find the cost of white washing the wall, if the rate of white washing the wall is Rs 20 per m2.

Question 9 : Find the area of each of the following parallelograms:
(a)
(b)
(c)
(d)
(e)

Question 10 : Find the area of each of the following triangles:
(a)
(b)
(c)
(d)

Question 11 : Find the missing values:
S.No. Base Height Area of the Parallelogram
a. 20 cm 246 cm2
b. 15 cm 154.5 cm2
c. 8.4 cm 48.72 cm2
d. 15.6 cm 16.38 cm2

Question 12 : Find the missing values:
Base Height Area of Triangle
15 cm 87 cm2
31.4 mm 1256 mm2
22 cm 170.5 cm2

Question 13 : PQRS is a parallelogram (Fig 11.23). QM is the height from Q to SR and QN is the height from Q to PS. If SR = 12 cm and QM = 7.6 cm. Find:
(a) The area of the parallelogram PQRS (b) QN, if PS = 8 cm

Question 14 : DL and BM are the heights on sides AB and AD respectively of parallelogram ABCD (Fig 11.24). If the area of the parallelogram is 1470 cm2, AB = 35 cm and AD = 49 cm, find the length of BM and DL.

Question 15 : ΔABC is right angled at A (Fig 11.25). AD is perpendicular to BC. If AB = 5 cm, BC = 13 cm and AC = 12 cm, Find the area of ΔABC. Also find the length of AD.

Question 16 : ΔABC is isosceles with AB = AC = 7.5 cm and BC = 9 cm (Fig 11.26). The height AD from A to BC, is 6 cm. Find the area of ΔABC. What will be the height from C to AB i.e., CE?

Question 17 : Find the circumference of the circles with the following radius. (Take π =227)
(a) 14 cm
(b) 28 mm
(c) 21 cm

Question 18 : Find the area of the following circles, given that (Take π =227)
(a) radius = 14 mm
(b) diameter = 49 m
(c) radius = 5 cm

Question 19 : If the circumference of a circular sheet is 154 m, find its radius. Also find the area of the sheet. (Take π =227)

Question 20 : 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 offence. Also find the cost of the rope, if it costs ₹ 4 per metre. (Take π =227)

Question 21 : From a circular sheet of radius 4 cm, a circle of radius 3 cm is removed. Find the area of the remaining sheet. (Take π = 3.14)

Question 22 : Saima wants to put a lace on the edge of a circular table cover of diameter 1.5 m. Find the length of the lace required and also find its cost if one metre of the lace costs ₹ 15. (Take π = 3.14)

Question 23 : Find the perimeter of the given figure, which is a semicircle including its diameter.

Question 24 : Find the cost of polishing a circular table-top of diameter 1.6 m, if the rate of polishing is ₹ 15 m2. (Take π = 3.14)

Question 25 : Shazli took a wire of length 44 cm and bent it into the shape of a circle. Find the radius of that circle. Also find its area. If the same wire is bent into the shape of a square, what will be the length of each of its sides? Which figure encloses more area, the circle or the square? (Take π =227)

Question 26 : From a circular card sheet of radius 14 cm, two circles of radius 3.5 cm and a rectangle of length 3 cm and breadth 1 cm are removed, (as shown in the given figure below). Find the area of the remaining sheet. (Take π = 227)

Question 27 : A circle of radius 2 cm is cut out from a square piece of an aluminium sheet of side 6 cm. What is the area of the left over aluminium sheet? (Take π = 3.14)

Question 28 : The circumference of a circle is 31.4 cm. Find the radius and the area of the circle. (Take π = 3.14)

Question 29 : A circular flower bed is surrounded by a path 4 m wide. The diameter of the flower bed is 66 m. What is the area of this path? (Take π = 3.14)

Question 30 : A circular flower garden has an area of 314 m2. A sprinkler at the centre of the garden can cover an area that has a radius of 12 m. Will the sprinkler can water the entire garden?
[Take π = 3.14]

Question 31 : Find the circumference of the inner and the outer circles, shown in the given figure. (Take π = 3.14)

Question 32 : How many times a wheel of radius 28 cm must rotate to go 352 m? (Take π = 227)

Question 33 : The minute hand of a circular clock is 15 cm long. How far does the tip of the minute hand move in 1 hour? (Take π = 3.14)

Question 34 : A garden is 90 m long and 75 m broad. A path 5 m wide is to be built outside and around it. Find the area of the path. Also find the area of the garden in hectare.

Question 35 : A 3 m wide path runs outside and around a rectangular park of length 125 m and breadth 65 m. Find the area of the path.

Question 36 : A picture is painted on a cardboard 8 cm long and 5 cm wide such that there is a margin of 1.5 cm along each of its sides. Find the total area of the margin.

Question 37 : A verandah of width 2.25 m is constructed all along outside a room which is 5.5 m long and 4 m wide. Find:
(i) the area of the verandah.
(ii) the cost of cementing the floor of the verandah at the rate of ₹ 200 per m2.

Question 38 : A path 1 m wide is built along the border and inside a square garden of side 30 m. Find:
(i) the area of the path.
(ii) the cost of planting grass in the remaining portion of the garden at the rate of ₹ 40 per m2.

Question 39 : Two cross roads, each of width 10 m, cut a right angles through the centre of a rectangular park of length 700 m and breadth 300 m and parallel to its sides. Find the area of the roads. Also find the area of the park excluding cross roads. Give the answer in hectares.

Question 40 : Through a rectangular field of length 90 m and breadth 60 m, two roads are constructed which are parallel to the sides and cut each other at right angles through the centre of the fields. If the width of each road is 3 m, find
(i) the area covered by the roads.
(ii) the cost of constructing the roads at of the rate of ₹ 110 per m2.

Question 41 : Pragya wrapped a cord around a circular pipe of radius 4 cm (adjoining figure) and cut off the length required of the cord. Then she wrapped it around a square box of side 4 cm (also shown). Did she have any cord left? (π = 3.14)

Question 42 : The adjoining figure represents a rectangular lawn with a circular flower bed in the middle. Find:
(i) the area of the whole land
(ii) the area of the flower bed
(iii) the area of the lawn excluding the area of the flower bed
(iv) the circumference of the flower bed.

Question 43 : In the following figures, find the area of the shaded portions:

Question 44 : Find the area of the quadrilateral ABCD.
Here, AC = 22 cm, BM = 3 cm,
DN = 3 cm, and
BM⊥AC, DN⊥AC