  # Grade 7 Maths Ncert solutions Perimeter and Area

NCERT books are recommended text book for CBSE school curriculum. Most of the govt aided and private schools in India follow NCERT text books as the syllabus books for school subjects. They are written by eminent academicians and scholars from leading universities and academic institutions in India, and help in building a strong base, as well help understand each concept by relevant examples and exercises. They are termed best in term of concept building, for their usage of real life practical examples, and good end of the chapter exercises.

In this article, we have shared solved NCERT exercises for Class 7 maths perimeter and area chapter.  Perimeter and area is an important chapter, as it set a base for the geometry for the future classes. These NCERT solutions will help students in solving their doubts and clarifying confusion regarding confusions regarding this chapter. Students can refer to NCERT solutions for perimeter and area chapter for their conceptual understanding, as well as matching their own answers with the right solutions of the exercises.

## Class 7 math ncert solution perimeter and area chapter

Exercise 11.1 solutions

Q1 – 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. View solution

Q2 – Find the area of a square park whose perimeter is 320 m. View solution

Q3 – 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. View solution

Q4 – The perimeter of a rectangular sheet is 100 cm. If the length is 35 cm, find its breadth. Also find the area. View solution

Q5 – 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. View solution

Q6 – 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? View solution

Q7 – 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. View solution

Q8 – A door of length 2 m and breadth 1m is fitted in a wall. The length of the wall is 4.5 m and the breadth is 3.6 m Find the cost of white washing the wall, if the rate of white washing the wall is Rs 20 per m2 View solution

Exercise 11.2 solutions

Q1 – Find the area of each of the following parallelograms: View solution

Q2 – Find the area of each of the following triangles: View solution

Q3 – Find the missing values: View solution

Q4 – Find the missing values: View solution

Q5 – PQRS is a parallelogram. 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 parallegram PQRS (b) QN, if PS = 8 cm View solution

Q6 – DL and BM are the heights on sides AB and AD respectively of parallelogram ABCD. If the area of the parallelogram is 1470 cm2 , AB = 35 cm and AD = 49 cm, find the length of BM and DL. View solution

Q7 – ∆ABC is right angled at A. AD is perpendicular to BC. If AB = 5 cm, BC = 13 cm and AC = 12 cm, Find the area of ∆ABC. Also find the length of AD. View solution

Q8 – ∆ABC is isosceles with AB = AC = 7.5 cm and BC = 9 cm. The height AD from A to BC, is 6 cm. Find the area of ∆ABC. What will be the height from C to AB i.e., CE? View solution

Exercise 11.3 solutions

Q1 – Find the circumference of the circles with the following radius: (Take π = 22/7) (a) 14 cm (b) 28 mm (c) 21 cm  View solution

Q2 – Find the area of the following circles, given that: (a) radius = 14 mm (Take π = 22/7) (b) diameter = 49 m (c) radius = 5 cm  View solution

Q3 – If the circumference of a circular sheet is 154 m, find its radius. Also find the area of the sheet. (Take π = 22/7) View solution

Q4 – A gardener wants to fence a circular garden of diameter 21m. Find the length of the rope he needs to purchase, if he makes 2 rounds of fence. Also find the cost of the rope, if it costs Rs 4 per meter. (Take π = 22/7) View solution

Q5 – 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) View solution

Q6 – 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 meter of the lace costs Rs 15. (Take π = 3.14) View solution

Q7 – Find the perimeter of the adjoining figure, which is a semicircle including its diameter. View solution

Q8 -Find the cost of polishing a circular table-top of diameter 1.6 m, if the rate of polishing is Rs 15/m2 . (Take π = 3.14) View solution

Q9. 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 = 22/7 ) View solution

Q10. 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 1cm are removed. Find the area of the remaining sheet. (Take π = 22/7) View solution

Q11 – 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) View solution

Q12 – The circumference of a circle is 31.4 cm. Find the radius and the area of the circle? (Take π = 3.14) View solution

Q13 – 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? (π = 3.14) View solution

Q14 – 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 water the entire garden? (Take π = 3.14) View solution

Q15 – Find the circumference of the inner and the outer circles, shown in the adjoining figure? (Take π = 3.14) View solution

Q16 – How many times a wheel of radius 28 cm must rotate to go 352 m? (Take π = 22/7) View solution

Q17 – 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) View solution

Exercise 11.4 solutions

Q1 – 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.  View solution

Q2 – 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.  View solution

Q3 – 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. View solution

Q4 – 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 Rs 200 per m2 . View solution

Q5 – 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 Rs 40 per m2 . View solution

Q6 – Two cross roads, each of width 10 m, cut at 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. View solution

Q7 – 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 the rate of Rs 110 per m2 . View solution

Q8 – 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) View solution

Q9 – 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. View solution

Q10 – Find the area of the shaded portions View solution

Q11 – Find the area of the quadrilateral ABCD. Here, AC = 22 cm, BM = 3 cm, DN = 3 cm, and BM ⊥ AC, DN ⊥ AC View solution

## End Note

In the article, we have shared solutions for ncert exercises for class 7 maths for perimeter and area chapter. Students can click to respective chapters and refer to the right solution. We advise students to refer to them as clearing their concepts, and matching their solutions. Student should not use them to copy solutions for their homework and instead should try to solve homework on own, as it will impact their learning process.

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