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06
NCERT Solutions · Maths Ch 6
Perimeter and Area
38 questions · 4 exercises
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Ex 6.1
Ex 6.2
Ex 6.3
Ex 6.4
NCERT answers with full exam-style working, step by step. Tap a question to open its solution.
1
EXERCISE 6.1 · 14 QUESTIONS
Perimeter
Q1
Find the missing terms: (a) Perimeter of a rectangle = 14 cm; breadth = 2 cm; length = ? (b) Perimeter of a square = 20 cm; side = ? (c) Perimeter of a rectangle = 12 m; length = 3 m; breadth = ?
(3 marks)
Q2
A rectangle having side lengths 5 cm and 3 cm is made using a piece of wire. If the wire is straightened and then bent to form a square, what will be the length of a side of the square?
(3 marks)
Q3
Find the length of the third side of a triangle having a perimeter of 55 cm and having two sides of length 20 cm and 14 cm.
(2 marks)
Q4
What would be the cost of fencing a rectangular park whose length is 150 m and breadth is 120 m, if the fence costs ₹40 per metre?
(2 marks)
Q5
A piece of string is 36 cm long. What will be the length of each side if it is used to form (a) a square, (b) a triangle with all sides of equal length, (c) a hexagon with sides of equal length?
(3 marks)
Q6
A farmer has a rectangular field of length 230 m and breadth 160 m. He wants to fence it with 3 rounds of rope. What is the total length of rope needed?
(2 marks)
Q7
Matha Pachchi: Akshi runs 5 rounds on the outer rectangular track (70 m × 40 m). Find the total distance she covered.
(2 marks)
Q8
Toshi runs 7 rounds on the inner rectangular track (60 m × 30 m). Find the total distance she covered. Who ran the longer distance?
(2 marks)
Q9
Mark positions: (a) 'A' where Akshi is after running 250 m; (b) 'B' after 500 m; (c) Akshi has run 1000 m: how many full rounds, and mark 'C'; (d) 'X' where Toshi is after 250 m; (e) 'Y' after 500 m; (f) Toshi has run 1000 m: how many full rounds, and mark 'Z'.
(5 marks)
Q10
Deep Dive: Two square running tracks, inner of side 100 m and outer of side 150 m, have a common finishing line at the middle of one side. In a 350 m race, find the starting points A (inner) and B (outer).
(3 marks)
Q11
Akshi says that the perimeter of a triangle drawn on a dot grid (sides along squares and a diagonal) is 9 units. Toshi says it will be more than 9 units. What do you think?
(2 marks)
Q12
Write the perimeters of the figures in terms of straight (s) and diagonal (d) units. (Triangle example: 6s + 3d.)
(2 marks)
Q13
Find perimeters of regular polygons: generalise the perimeter of a regular polygon (the perimeter of an equilateral triangle is 3 × side).
(2 marks)
Q14
Split and rejoin: a 6 cm × 4 cm rectangular chit is cut into two equal pieces and rejoined in different ways. Arrangement (a) has perimeter 28 cm. How do we find the perimeter of the others, and how can the pieces be arranged to give a perimeter of 22 cm?
(3 marks)
2
EXERCISE 6.2 · 7 QUESTIONS
Area
Q1
The area of a rectangular garden 25 m long is 300 sq m. What is the width of the garden?
(2 marks)
Q2
What is the cost of tiling a rectangular plot of land 500 m long and 200 m wide at the rate of ₹8 per hundred sq m?
(2 marks)
Q3
A rectangular coconut grove is 100 m long and 50 m wide. If each coconut tree requires 25 sq m, what is the maximum number of trees that can be planted in this grove?
(2 marks)
Q4
By splitting the following figures into rectangles, find their areas (all measures in metres): (a) a figure with sides 3, 1, 2, 2, ... (b) a figure with sides 5, 2, 3, 3, 4, 4, 3, 1, 1, ...
(1 mark)
Q5
Find the area of the figures drawn on squared paper (estimate using the rule: count full squares, count squares more than half, count exactly half as 1, ignore less than half).
(1 mark)
Q6
On squared paper make rectangles, with whole-number sides, of area 24 sq units. (a) Which has the greatest perimeter? (b) Which has the least? (c) Repeat for area 32 sq cm.
(5 marks)
Q7
Example (textbook): A floor is 5 m long and 4 m wide. A square carpet of side 3 m is laid. Find the area not carpeted.
(2 marks)
3
EXERCISE 6.3 · 7 QUESTIONS
Area of a Triangle
Q1
Find the areas of the figures by dividing them into rectangles and triangles. (Five figures a to e.)
(3 marks)
Q2
Triangle and rectangle: in rectangle ABCD, a diagonal BD divides it into two triangles. State the relationship between the area of triangle BAD and rectangle ABCD, and also for triangle ABE where E lies on side DC.
(3 marks)
Q3
Using 9 unit squares, make figures (squares joined along full sides, one connected figure, no holes). (1) What is the smallest perimeter possible? (2) What is the largest? (3) Make a figure with perimeter 18 units. (4) Can you make other shapes for each of these perimeters?
(2 marks)
Q4
A figure has perimeter 24 units. If a new square is attached to it, what happens to the perimeter? Can you place the square so that the perimeter (a) increases, (b) decreases, (c) stays the same?
(3 marks)
Q5
Charan's house plan (rectangular plot 35 ft × 30 ft): find the missing measurements and area of each room, and the area of the house.
(5 marks)
Q6
Sharan's house (plot 42 ft long): find the missing dimensions and the area. Compare the areas and perimeters of Sharan's and Charan's houses.
(3 marks)
Q7
Area Maze Puzzles: in each figure find the missing value of either a side or the area of a region.
(2 marks)
4
EXERCISE 6.4 · 10 QUESTIONS
End of Chapter
Q1
Give the dimensions of a rectangle whose area is the sum of the areas of two rectangles of 5 m × 10 m and 2 m × 7 m.
(3 marks)
Q2
The area of a rectangular garden that is 50 m long is 1000 sq m. Find the width of the garden.
(2 marks)
Q3
The floor of a room is 5 m long and 4 m wide. A square carpet of side 3 m is laid on the floor. Find the area that is not carpeted.
(2 marks)
Q4
Four flower beds having sides 2 m long and 1 m wide are dug at the four corners of a garden that is 15 m long and 12 m wide. How much area is available for laying down a lawn?
(2 marks)
Q5
Shape A has an area of 18 square units and Shape B has an area of 20 square units. Shape A has a longer perimeter than Shape B. Draw two such shapes.
(2 marks)
Q6
On a page in your book, draw a rectangular border that is 1 cm from the top and bottom and 1.5 cm from the left and right sides. What is the perimeter of the border?
(3 marks)
Q7
Draw a rectangle of size 12 units × 8 units. Draw another rectangle inside it, without touching the outer rectangle, that occupies exactly half the area.
(2 marks)
Q8
A square piece of paper is folded in half and cut along the fold into two rectangles. Which statement is always true? (a) The area of each rectangle is larger than the area of the square. (b) The perimeter of the square is greater than the perimeters of both rectangles added together. (c) The perimeters of both rectangles added together is always 1½ times the perimeter of the square. (d) The area of the square is always three times as large as the areas of both rectangles added together.
(3 marks)
Q9
Tangram: with the seven tangram pieces A to G (A, B large triangles; C, E small triangles; D medium triangle; F square; G parallelogram), (1) how many pieces have the same area? (2) How many times bigger is D than C? (3) D or F — which is larger? (4) F or G? (5) Area of A compared to G? (6) Area of the big square in terms of C? (7) The rectangle formed? (8) Perimeters of the square and the rectangle?
(3 marks)
Q10
Why is area generally measured using squares and not circles?
(2 marks)