Class 7 ( CBSE ) / Chap 11 /Perimeter & Area. Chapter Facts. 1. Perimeter of a rectangle = 2 (length + breadth) 2. Perimeter of a square = 4 length of its side. Also, side of a square = perimeter 4 3. Perimeter of an equilateral triangle = 3 length of a side. Also, side of an equilateral triangle = perimeter 3 4. Perimeter of triangle = sum of lengths of three sides. Perimeter ABC = a + b + c. 5. Perimeter of parallelogram = 2 x sum of lengths of adjacent sides. Perimeter gm ABCD = 2 x ( a + b ) 6. Circumference of a circle =2 r = d [ π = 22/7 or 3.14 ] 9. Distance covered by a wheel in n rotations = n x circumference = n x 2 r. 10. Area of a rectangle = length breadth 11. Area of square = side x side or side 2. 12. Area of a triangle = ½ base corresponding height Area ABC =½ BC h 13. Area of a quadrilateral = ½ x ( diagonal ) x ( sum of offsets) Note : - perpendiculars let fall from opposite vertices are called offsets. area ABCD = ½ x AC x (BL + CM ) 14. Area of a parallelogram = base height Area gm ABCD = a x h 15. Number of tiles needed to cover a floor = 16. Area of a circle = r 2 area of area of floor one tile
17. Two circles having same center but different radii are called concentric circles. The region between two concentric circles is called its annulus. Area of annulus of a circle= π( R + r ) ( R r ) 18. Area can be converted from one unit to another using the following figure.. Formative Assessment A ) Multiple Choice Questions Tick ( ) the correct answer for each of the following : 1. The perimeter of a rectangle whose area and breadth are respectively 432 cm 2 and 18 cm, is (a) 84 cm (b) 24 cm (c) 108 cm (d) 42 cm 2. The area of a square park whose perimeter is 380 m is (a) 10925 m 2 (b) 7225 m 2 (c) 9025 m 2 (d) 9050 m 2 3. The ratio of circumference of two circles whose radii are in the ratio 4 : 3 is (a) 4 : 3 (b) 4 : 5 (c) 16 : 9 (d) 9 : 16 4. The height of a parallelogram whose area and corresponding base are respectively 250 cm and 20 cm is (a) 12.5 cm (b) 25 cm (c) 18 cm (d) 30 cm 5. The area of a circle of diameter 42 cm is (a) 1386 cm 2 (b) 693 cm 2 (c) 2772 cm 2 (d) 5544 cm 2 6. The area of a right triangle whose legs are 8 cm and 4.5 cm in length is (a) 36 cm2 (b) 18 cm 2 (c) 24 cm 2 (d) 48 cm 2 7. The perimeter of a field in shape of a rectangle with adjacent sides 12 m and 7 m is (a) 34 cm (b) 17 cm (c) 23 cm (d) 38 cm 8. The circumference of a circular disc of radius 35 cm is (a) 220 cm (b) 110 cm (c) 3580 cm (d) 440 cm 9. The base of a triangle whose area and corresponding altitude are respectively 390 m and 24 m, is (a) 16.25 cm (b) 32.5 m (c) 36 cm (d) 38 m 10. A circular disc of radius 10.5 cm was divided in two equal semicircles. The perimeter of each semicircular shape disc is (a) 33 cm (b) 43.5 cm (c) 54 cm (d) 66 cm 11. If we increase the perimeter of a figure, its area (a) will also increase (b) will decrease (c) will remain same (d) may increase or decrease 12. There is a path 4 m wide around a circular park of radius 50 m. The diameter of the outer circle is (a) 128 m (b) 58 m (c) 104 m (d) 108 m
13. The cost of leveling a rectangular field 105 m long and 90 m wide at the rate of Rs 65 per m 2 is (a) Rs 25350 (b) Rs 12675 (c) Rs 614250 (d) Rs 307125 14. The cost of fencing a square lawn 88 m in length at the rate of Rs 42.5 per m is (a) Rs 14960 (b) Rs 29920 (c) Rs 329120 (d) Rs 164560 15. The radius of a circle of area 707 7 1 cm 2 is (a) 50 cm (b) 45 cm (c) 30 cm (d) 15cm 16. The number of squares of side 3 cm required to cover a rectangle measuring 33 cm by 12 cm are (a) 132 (b) 66 (c) 44 (d) 22 17. The base of parallelogram is twice is height. If its area is 722 m 2, the base and height of the parallelogram are respectively. (a) 19 m and 38 m (b) 38 m and 19 m (c) 16 m and 32 m (d) 36 m and 18 m 18. The diameter of a wheel of a car is 70 cm. The number of complete revolutions it will take to travel 8 km is (a) 3600 (b) 3625 (c) 3636 (d) 3650 19. A floor 26 m by 14 m is to be covered by tiles 28 cm by 13 cm. How many tiles are required? (a) 10000 (b) 20000 (c) 5000 (d) 2500 20. A circular path 2 m wide is built around a circular pond of diameter 6 m. The area of the path is ( use π = 3.14 (a) 50.24 m 2 (b) 100.48 m 2 (c) 62.8 m 2 (d) 36.5 m 2 B ) Fill in the blanks: Give the formula for each of the following ( 1-12 ) 1. Perimeter of square = 2. Area of square = 3. Perimeter of rectangle = 4. Area of rectangle = 5. Perimeter of triangle = 6. Area of triangle = 7. Area of quadrilateral = 8. Perimeter of parallelogram = 9. Area of parallelogram = 10. Circumference of circle = 11. Area of circle = 12. Area of annulus = Convert ( 13 22 ) 13. 1000 mm 2 = cm 2. 14. 2000 cm 2 = dm 2. 15. 30000 cm 2 = m 2. 16. 400 dm 2 = m 2. 17. 6000000 m 2 = km 2. 18. 4 cm 2 = mm 2. 19. 5 dm 2 = cm 2. 20. 3 m 2 = cm 2. 21. 5 m 2 = dm 2. 22. 7 km 2 = m 2. C) True / False
Say true or false for each of the following. State true (T) or false (F) for each of the following statements : 1. An increase in the perimeter need not lead to increase in area of a figure. T/F. 2. All the congruent figures are equal in area. T/F 3. The triangles equal in area are congruent. T/F 4. Rectangle with same perimeter have equal areas. T/F 5. The circumference of a circle is equal to times its diameter. T/F 6. 22 7 is the exact value of. T/F 7. The perimeter of a semi circular disc is 1 r. 2 T/F D ) True / False with Justification : Say true or false for each of the following. Justify your answer? 1. If we draw a margin 2 m wide, outside a square of side 20 cm, then the side of the new square will be 22 cm. T/F 2. The circumference of a circle is always more than three times its diameter. T/F 3. Area of a triangle is twice the area of the parallelogram with same base and height. T/F 4. If two figures are equal in area they are congruent. T/F E ) Matching Match items in column I with items in column II. Column I Column II (a) Area of a triangle with base 10 cm and (i) 50 sq.cm corresponding height 8 cm. (b) Area of a quadrilateral with diagonal 10 cm and (ii) 154 sq.cm offsets let fall on the diagonal are 4 cm and 6 cm. (c) Area of a square with perimeter 80 cm. (iii) 60 sq. cm (d ) Area of a circle with radius 7 cm. (iv) 120 sq.cm (e ) Area of a gm with base 12 cm and (v) 400 sq. cm corresponding height 10 cm. (vi) 40 sq. cm. Summative Assessment A ) One mark questions 1. Find the perimeter of a triangle with sides 4 cm, 5 cm and 6 cm.
2. Find the area of a triangle with side 4 cm and corresponding height 5 cm. 3. Find the perimeter of a square with side 9 dm. 4. Find the area of a square with side 8 dm. 5. Find the perimeter of a rectangle with length 10 m and breadth 6m. 6. Find the area of a rectangle with length 5 m and breadth 3m. 7. Diagonal of a quadrilateral is 12 cm and perpendiculars let fall on it form opposite vertices are 8 cm and 6 cm. Find its area. 8. Radius of a circle is 7 dm. Find its circumference. 9. Radius of a circle is 10 cm. Find its area. ( use = 3.14 ) 10. Inner and outer radii of an annulus of a circle are 4cm and 3 cm. Fin the area of the annulus. B ) Two mark questions. 1. Area of a triangle is 32 cm 2. If one of its side is 8 cm, find the corresponding height. 2. Area of square is 121 dm 2. Find its perimeter. 3. Perimeter of a square is 220 cm 2. Find its area. 4. Perimeter of a rectangle is 20 m. If its length is 8m, find its area. 5. Area of a rectangle with length 10 dm is 60 dm 2. Find its perimeter. 6. Circumference of a circle is 44 cm. Find its area. 7. Area of a circle is 314 cm 2. find its circumference. (π = 3.14 ) 8. A door-frame of dimensions 3 m 2 m is fixed on the wall of dimension 10 m 10 m. Find the total labour charges for painting the wall if the labour charges for painting 1 m 2 of the wall is Rs 2.50. 9. The area of a rectangular sheet is 500 cm 2. If the length of the sheet is 25 cm, what is its width? Also find the perimeter of the rectangular sheet. 10. Ritu wants to fence the garden in front of her house on three sides with lengths 20 m, 11 m and 12 m. Find the cost of fencing at the rate of Rs 150 per metre. C ) Three mark questions 1. A wire is in the shape of a square of side 10 cm. If the wire is re-bent into a rectangle of length 12 cm, find its breadth. Which encloses more area, the square or the rectangle? 2. The area of a square and a rectangle are equal. If the side of the square is 40 cm and the breadth of the rectangle is 25 cm, find the length of the rectangle. Also, find the perimeter of the rectangle. 3. 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? ( = 3.14) 4. On 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 drawn such that no two of these overlap. Now these are cut out. Find the area of the remaining sheet. 5. How many times a wheel of radius 28 cm must rotate to go 176 m? 6. The minute hand of a circular clock is 10 cm long. How far does the tip of the minute hand move in 1 hour. ( = 3.14) D ) Four mark questions
1. A wire of length 44 cm and bent it into the shape of a circle. 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? 2. A circular flower garden has an area of 314 m 2. A sprinkler at the centre of the garden can cover an area that has a radius of 8m. What part of the garden will be left unwatered? ( = 3.14) 3. A rectangular park is 45 m long and 20 m wide. A path 2.5 m wide is constructed outside the park. Find the area of the path. 4. A picture is painted on a cardboard 15 cm long and 12 cm wide such that there is a margin of 2 cm along each of its sides. Find the total area of the margin. 5. Two cross roads, each of width 5 m, run at right angles through the centre of a rectangular park of length 100 m and breadth 50 m and parallel to its sides. Find the area of the roads. Also find the cost of constructing the roads at the rate of Rs 100 per m 2. End Answers Formative Assessment A ) Multiple Choice Questions 1 a 2 c 3 a 4 a 5 a 6 b 7 d 8 a 9 b 10 c 11 a 12 a 13 c 14 a 15 d 16 c 17 b 18 c 19 a 20 a B ) Fill in the blanks: 1 4 x side 2 side 2 3 2 ( L + B ) 4 L x B 5 a + b + c 6 ½ x base x corresponding height 7 ½ x diagonal x sum of offsets 8 2 ( a + b ) 9 base x corresponding height 10 2 r 11 r 2 12 ( R + r ) ( R r ) 13 10 14 20 15 3 16 4 17 6 18 400 19 500 20 30000 21 500 22 7000000 C ) True/ False 1 T 2 T 3 F 4 F 5 T 6 F 7 F D ) True / False with Justification : 1. F ; Perimeter will be ( 2 + 20 + 2 ) cm = 24 cm 2. T ; C = 2 r = D = 3.14 x D > 3 D 3. T ; fig area ABC = ½ x ( base x h ) = ½ x area gm ABCD 4. F ; consider fig
area ABC = ½ x 4 x 8 cm 2 = 16 cm 2. Area DEFG = 8 x 2 cm 2 = 16 cm 2 Both are equal in area but not congruent. E ) Matching (a) vi, (b) i, (c) v, (d) ii, (e) (iv) Summative Assessment A ) One mark questions 1 15 cm 2 10 cm 2 3 36 dm 4 64 dm 2 5 32 m 6 15 m 2 7 84 cm 2 8 44 dm 9 314 cm 2 10 22 cm 2 B ) Two mark questions. 1 8 cm 2 44 dm. 3 3025 m 2 4 16 m 2 5 32 dm. 6 154 cm 2 7 62.8 cm 8 Rs 235 9 20 cm, 90 cm 10 Rs 6600 C ) Three mark questions 1 8 cm, square 2 64 cm, 178 cm 3 879.2 m 2 4 11 cm, circle 5 536 cm 2 6 100 D ) Four mark questions 1 11 cm, circle 2 113.04 m 2 3 350 m 2. 4 92 cm 2 5 725 m 2 ; Rs 72500 m 6