FBE05 – Mathematics and Statistics Lecture 3 - Discovering Area

Introduction Area is defined as the amount of space taken up by a two-dimensional figure. The geometrical properties of triangles, quadrilaterals and circles. A summary of the formulae used in calculating the areas and other properties of these geometrical shapes is given in Table 11.1. The units of area used in metric systems are: mm2, cm2, m2

Area

Area

Area of triangles Find the area of the triangles shown in Figure 3.1:

Area of quadrilaterals A plane figure bounded by four straight lines is called a quadrilateral. The calculation of area of some of the quadrilaterals is explained in this section.

Area of circles The following formula is used for calculating the area of a circle: Area of a circle πr2 where r is the radius of the circle. Figure below shows a circle having a diameter of 4 m. Find: (a) the area of the circle (b) the area of the major and minor sectors

Area of circles Figure below shows a circular concrete path (shaded) around a lawn. Find the area of the path.

Application of area to practical problems Figure below shows the cross-section of a steel girder. Calculate its area in cm2 and mm2.

Application of area to practical problems The floor of a kitchen, measuring 3.20 m x 3.00 m, is to be finished with marble effect floor tiles each measuring 330 mm x 330 mm. If there are nine tiles in a pack, calculate the number of packs required. Allow 10% for wastage. The floor of a room, measuring 6.0 m x 4.2 m, is to be covered with laminate flooring. If one pack covers an area of 2.106 m2, calculate the number of packs required. Consider wastage @ 10%.

Application of area to practical problems The 3D view of a room is shown in Figure 3.7. The internal wall and ceiling surfaces require a coat of emulsion paint. Calculate their areas in m2. Given: Size of the door = 2m x 1m wide Height of the skirting board = 100 mm

Application of area to practical problems Cavity walls The cavity wall of a domestic building consists of brickwork as outer leaf and blockwork as inner leaf and the cavity between the two filled with Rockwool. The outer leaf of brickwork is 103mm thick (also called half brick thick wall). The inner leaf of concrete blocks is 100 mm thick. The measurements of bricks and concrete blocks used in area calculations are shown in Figure 3.10. The number of bricks and concrete blocks per m2 are 60 and 10 respectively.

Application of area to practical problems A cavity wall 5.4 m long and 2.7 m high (Figure 3.10) is to be constructed using facing bricks and aerated concrete blocks. Find the number of bricks and blocks required. Allow 5% extra for wastage.

Figure 3.10