1State whether each sentence is true or false: (a) The perimeter of a rectangle is found by adding its length and its breadth. (b) A book 15 cm long and 10 cm wide has a perimeter of 50 cm. (c) A table 6 m long and 2 m wide has a perimeter of 12 m. (d) A rectangle 2 m long and 1 m wide has a perimeter of 6 m. (e) The perimeter of a square is found by multiplying its side by 4. (f) A square handkerchief of side 5 m has a perimeter of 25 m. (g) A square of perimeter 4 m has a side of 1 m.
2Find the perimeter of the rectangles and squares with these measurements: (a) AB = 8 cm, BC = 5 cm (b) AB = 15 m, BC = 5 m (c) PQ = 9 cm, QR = 6 cm (d) XY = 12.5 ft, YZ = 7 ft (e) AB = 28 cm, BC = 15 cm (f) AB = 35 ft, BC = 35 ft (g) QR = RS = 40 m
3Find the perimeter of these shapes: (a) a rectangle 3 cm by 2 cm (b) a rectangle 5 cm by 3 cm (c) a square of side 4.5 m (d) a rectangle 18.5 ft by 13.5 ft
4A rectangular towel is 190 cm long and 110 cm wide. What is its perimeter?
5A rectangular field is 27 ft long and 22 ft wide. Find its perimeter.
6A square handkerchief has a side of 25 cm. What is its perimeter?
7A rectangular ground has a perimeter of 360 m and a breadth of 60 m. What is its length?
8A rectangular bed has a perimeter of 22 ft and a length of 6 ft. What is its breadth?
9The length of a rectangular plot is double its breadth and its perimeter is 42 m. Find its length and breadth.
10A square has a perimeter of 84 cm. What is the length of its side?
11Three hundred and forty trees are planted at equal distances all round a square field. How many trees stand along one side of the field?
12Fill in the blanks: (a) Squaring the side of a square shape gives its ......... . (b) If the length and breadth of a rectangular object are in centimetres, the unit of area is ......... . (c) A sheet of paper 3 m long and 2 m wide covers ......... . (d) The area of a paper 5 cm long and 3 cm wide is ......... . (e) A square cloth of side 2 m has an area of ......... square metres. (f) The area of an irregular surface is found by the ......... method.
13Find the area of the shapes drawn on graph paper by counting unit squares.
14Find the area of these rectangles and squares: (a) 5 cm by 3 cm (b) 18 cm by 7 cm (c) a square of side 19 cm (d) 11.5 m by 14.2 m
15Find the missing length or breadth of these rectangles: (a) length = 7 ft, area = 21 square feet (b) length = 18 cm, area = 90 square centimetres (c) breadth = 3.2 m, area = 38.4 square metres (d) breadth = 1 ft, area = 15 square feet
16Find the side of each square: (a) area = 1 square centimetre (b) area = 121 square feet (c) area = 196 square metres (d) area = 625 square metres
17Find the area of the shaded part: (a) a 6 cm by 4 cm rectangle with a blank 3 cm by 2 cm rectangle inside (b) a 10 cm by 8 cm rectangle with a blank 5 cm by 3 cm rectangle inside (c) a 5 cm by 5 cm square with a blank 2 cm by 1 cm rectangle inside (d) a 12.5 cm by 6 cm rectangle with a blank 6 cm by 5 cm rectangle inside
18Find the volume of these solids: (a) 5 cm by 3 cm by 4 cm (b) 7 cm by 1 cm by 2 cm (c) 8 cm by 8 cm by 8 cm (d) 13.5 cm by 5 cm by 6 cm
19Find the volume of the cuboids with these measurements: (a) 12 cm, 8 cm, 4 cm (b) 25 ft, 15 ft, 5 ft (c) 3.5 m, 2.2 m, 2 m (d) 16 cm, 10.5 cm, 5.5 cm
20Find the volume of the cubes whose edges are: (a) 1 m (b) 7 cm (c) 16 ft (d) 29 m
21A rectangular box is 55 cm long, 40 cm wide and 25 cm high. What is its volume?
22A cubical box has an edge of 17 cm. Find its volume.
23A cubical object has a volume of 64 cubic metres. What is the length of one edge?
24The length of a cuboid is double its breadth and its height is 2 ft. Its volume is 100 cubic feet. Find its length and breadth.
25A rectangular towel is 1 m 20 cm long and 80 cm wide. Find its perimeter and its area.
26A rectangular field has an area of 85 square feet and a breadth of 5 ft. Find its perimeter.
27A square has a side of 45 cm. Find its perimeter and its area.
28A rectangular ground has a perimeter of 280 m and a breadth of 50 m. Find its length and its area.
29A square has an area of 196 square centimetres. Find its side and its perimeter.
30The length of a rectangular plot is double its breadth and its area is 648 square metres. Find its length, its breadth and its perimeter.
31A cubical object has a volume of 1331 cubic centimetres. What is the length of its edge?
32The length of a cuboid is double its breadth and its height is 5 m. Its volume is 250 cubic metres. Find its length and breadth.
33A square and a rectangle have equal areas. The area of the square is 16 square metres and the side of the square is half the length of the rectangle. What is the breadth of the rectangle?
34A room has a floor 5 m long and 4 m wide. How much carpet is needed to cover the whole floor, and how long a strip is needed to run all round the edge of the floor?
35A rectangle turns out to have both a perimeter and an area whose number is 16. What are its length and breadth, and why are the units of the two answers different?
36The outline of a stone traced on graph paper covers 26 whole squares, and the part squares along its edge join up to make about 9 more. What is the area of the stone?