Perimeter and Area

Perimeter is the distance around a closed figure and area is the surface it covers. A rectangle has perimeter 2 x (l + b) and area l x b, and a square has perimeter 4 x side and area side x side. In this chapter, area formulas are extended to the parallelogram and the triangle. A parallelogram can be cut and rearranged into a rectangle, so its area is base x height. A diagonal divides a parallelogram into two congruent triangles, so the area of a triangle is 1/2 x base x height, where the height is the perpendicular from the opposite vertex. The chapter then studies the circle. The distance around a circle is its circumference, C = 2 x pi x r, and its area is pi x r x r, where r is the radius and pi is about 22/7 or 3.14. You also convert units, remembering that 1 square cm = 100 square mm and 1 hectare = 10000 square m, and find areas of paths, borders and fencing costs.

Detailed Worksheet: Perimeter and Area Section A - Definitions (10 marks) 1. Define perimeter and area. Write their units. (2 marks) 2. Write the formula for the area of a parallelogram and explain what base and height mean. (2 marks) 3. Write the formula for the area of a triangle. Why does it have a factor of 1/2? (2 marks) 4. What is the circumference of a circle? Write the formula for circumference and area of a circle. (2 marks) 5. Convert: (i) 5 square cm to square mm (ii) 3 hectares to square m. (2 marks) Section B - Calculations and Applications (15 marks) 6. The length and breadth of a rectangular park are 50 m and 40 m. Find (i) its area (ii) its perimeter (iii) the cost of fencing it at Rs 12 per m. (3 marks) 7. Find the area of a parallelogram with (i) base 7 cm and height 4 cm (ii) base 5 cm and height 4.8 cm (iii) base 2.5 cm and height 3.5 cm. (3 marks) 8. Find the area of a triangle with (i) base 15 cm and height 8 cm (ii) base 3.4 cm and height 5 cm. Also find the height of a triangle with area 36 square cm and base 9 cm. (3 marks) 9. Find the circumference and area of a circle of radius 14 cm (take pi = 22/7). Also find the radius of a circle whose circumference is 88 cm. (3 marks) 10. A rectangular garden 90 m by 75 m has a path 5 m wide outside it all around. Find the area of the path. (3 marks) Section C - Diagrams (10 marks) 11. Draw a parallelogram ABCD with base AB = 6 cm and height 4 cm. Show how cutting a right triangle from one side and joining it on the other side gives a rectangle. Find its area. (4 marks) 12. Draw a triangle ABC with base BC = 6 cm, and draw its altitude from A. Show a second altitude from B on side AC extended if the triangle is obtuse. (3 marks) 13. Draw a circle of radius 3.5 cm, mark the centre, a radius and a diameter. Find its circumference. (3 marks) Section D - Analysis and Higher-order Thinking (15 marks) 14. A wire is in the shape of a rectangle 40 cm long and 22 cm wide. It is rebent into a square. (i) Find the length of the wire. (ii) Find the side of the square. (iii) Which shape encloses more area and by how much? (iv) What general idea does this show? (5 marks) 15. Two cross roads, each 10 m wide, cross at right angles through the centre of a rectangular park 700 m by 300 m, parallel to its sides. (i) Find the area of the road along the length. (ii) Find the area of the road along the breadth. (iii) Find the total area of the roads, remembering the overlap. (iv) Find the area of the park excluding the roads. (5 marks) 16. A circular flower bed has a radius of 7 m. A circular path 3.5 m wide runs around it. (i) Find the area of the flower bed. (ii) Find the outer radius. (iii) Find the area of the path. (iv) Find the cost of tiling the path at Rs 10 per square m. (5 marks) Instructions: Time allowed 2 hours. Attempt all sections. Use pi = 22/7 unless stated, and write the correct unit with every answer.