3 rd Year Quick Questions 8/6/04

PERIMETER/AREA FORMULAE - REVISION 1. Rectangle Area = length ´ breadth 2. Square 3. Triangle

Example 1 Find the area of this triangle.

4. Circle (a) Perimeter Circumference (C) C = p x D p = 3.14159 ... Sometimes we use p = 3.14 (rounded to 3 significant figures)

Example Calculate the circumference of the following circle. C = p ´ D = p ´ 7 = 21.991... r = 3.5 cm = 22.0 cm (to 3 sig. figs) D = 7 cm

(b). Finding the Area of a Circle For all circles, the area can be found by using this formula. Area =   radius  radius A =  r²

EXAMPLES 2.5m 7cm A = r² A = r² = 153.938… = 19.634….. A = 154 cm² =   7  7 =   2.5  2.5 = 153.938… = 19.634….. A = 154 cm² A = 19.6 m²

A = r² A = r² 6.4m 16cm r = 8cm r = 3.2m = 201.061…. = 32.169…. =  8 8 = 3.2 3.2 = 201.061…. = 32.169…. A = 201cm² A = 32.2m²

MORE EXAMPLES 4.3m A = r² A = r² = 2.4 2.4 = 4.3 4.3 2.4m 1. Area of large circle Area of small circle 4.3m A = r² A = r² = 2.4 2.4 = 4.3 4.3 2.4m = 58.088… = 18.095…. A = 58.1m² A = 18.1m² Shaded area = 58.1m² - 18.1m² Find the shaded area. Shaded area= 40m²

24cm Find the shaded area. Square A=2424 = 576cm² 1 circle r =6cm 2. 24cm Find the shaded area. Square A=2424 = 576cm² 1 circle r =6cm A= r² =  6 6 A= 113.097… 24cm Area of 4 circles = 113.097 4 = 452.388 Shaded area = 576cm² - 452cm² = 452cm² = 124cm²

Find the perimeter and the area of this shape. 3. 10cm Find the perimeter and the area of this shape. 4cm Area Perimeter Circle Rectangle C = d A= r² A= 4  10 =   10 =   5  5 = 40cm² = 78.5cm² = 31.4cm Perimeter = 31.4 + 4 + 4 Total area = 78.5 + 40 = 118.5cm² = 39.4cm

area of rectangle – area of semi-circle 4. Find the shaded area. 60cm 40cm Shaded area area of rectangle – area of semi-circle r =30cm A = 60  40 A= r²  2 = 2400cm² =  30 30 2 = 1413.7… = 1414cm² Shaded area = 2400 - 1414 = 986cm²