Mensuration

Mensuration deals with measuring the size of plane figures. In this chapter you first study perimeter, the distance covered along the boundary of a closed figure when you go round it once. You will find the perimeter of any polygon by adding its sides, and learn the formulas for a rectangle, perimeter = 2 x (length + breadth), and a square, perimeter = 4 x side. For regular shapes such as an equilateral triangle or a regular pentagon, the perimeter is the number of sides multiplied by the length of one side. The chapter then introduces area, the amount of surface enclosed by a closed figure, measured in square units such as square centimetres. You will estimate area on squared paper, counting a full or more-than-half square as 1, a half square as 1/2, and ignoring less than half. Finally, you will use area of a rectangle = length x breadth and area of a square = side x side to solve problems on fencing, tiling and painting.

Detailed Worksheet: Mensuration Section A - Definitions (10 marks) 1. Define perimeter. Why is the perimeter measured in units of length such as cm or m? (2 marks) 2. Define area. In what units is area measured? (2 marks) 3. Write the formulas for the perimeter of a rectangle and a square, explaining each term. (2 marks) 4. What is a regular closed figure? Write the formula for the perimeter of a regular hexagon of side s. (2 marks) 5. Write the formulas for the area of a rectangle and a square. How is area different from perimeter? (2 marks) Section B - Calculations and Applications (15 marks) 6. Find the perimeter of: (i) a rectangle of length 15 cm and breadth 9 cm (ii) a square of side 7.5 cm (iii) a triangle with sides 4 cm, 6 cm and 7.5 cm. (3 marks) 7. A rectangular park is 175 m long and 125 m wide. Find the cost of fencing it at the rate of Rs 12 per metre. (3 marks) 8. Find the area of: (i) a rectangle 12 m long and 8 m wide (ii) a square plot of side 15 m (iii) a rectangle 3 m long and 70 cm wide, in square centimetres. (3 marks) 9. The area of a rectangular garden 50 m long is 300 square metres. Find its width. Also find the cost of putting a fence around it at Rs 10 per metre. (3 marks) 10. How many tiles, each 12 cm by 5 cm, are needed to cover a rectangular region 144 cm long and 100 cm wide? (3 marks) Section C - Diagrams (10 marks) 11. On squared paper, draw a rectangle 6 units by 4 units and a square of side 5 units. Find the perimeter and area of each. Which has the larger perimeter and which has the larger area? (4 marks) 12. Draw an irregular leaf shape on squared paper (or describe one covering about 10 full squares, 6 more-than-half squares and 4 exactly-half squares). Use the rule for counting squares to estimate its area. (3 marks) 13. Draw an L-shaped figure formed by a rectangle 8 cm long and 3 cm high, with a second rectangle 3 cm wide and 4 cm high standing on top of it at its left end. Mark all the side lengths and find its perimeter and area. (3 marks) Section D - Analysis and Higher-order Thinking (15 marks) 14. Bushra needs to put a lace border all around a rectangular table cover 3 m long and 2 m wide. (i) Find the length of lace required. (ii) If lace costs Rs 15 per metre, find the cost. (iii) Find the area of the table cover. (iv) Another cover is a square with the same perimeter; find its side and area and compare. (5 marks) 15. A square and a rectangle each have perimeter 40 cm. The rectangle has length 14 cm. (i) Find the breadth of the rectangle. (ii) Find the side of the square. (iii) Find the area of each. (iv) Which shape encloses more area? What general idea does this suggest? (5 marks) 16. A wire is in the shape of a square of side 10 cm. It is straightened and bent into a rectangle of length 12 cm. (i) Find the length of the wire. (ii) Find the breadth of the rectangle. (iii) Compare the areas of the square and rectangle. (iv) Explain why the perimeter stays the same but the area changes. (5 marks) Instructions: Time allowed 2 hours. Attempt all sections. Write the correct unit with every answer and convert all measurements to the same unit before calculating.