Knowledge of quantities / calculating areas

Knowledge of technical information, quantities and communicating with others

Materials calculations Area - calculations Rectangle Area is used in construction for costing work and estimating quantities. It is normally measured in squared metres. A square metre is the surface of a square measuring 1 metre by 1 metre, and is written as 1m2. It is calculated by multiplying the two sides together. It is the space that counts the area, not the shape. 2m 0.5m 1m 4m 0.25m

Materials calculations Area - calculations Squares All areas of squares and rectangles are worked out in the same way. You simply multiply the length by the height 5m x 2m = 10m2 3.5m x 2m = 7m2 3m x 4m = 12m2 2.5m x 4m = 10m2

Materials calculations Take out area 4m 3m Step 1: Work out the total area: 4m x 3m = 12 m2 Step 2: Work out the area of the opening(s): 2m x 1m = 2m2 Step 3: Take the openings from the total area: 12m2 – 2m2 = 10m2 The area of the wall is 10m2 12m2 2m2 2m2 10m2

Materials calculations Formula - rectangles L Area = Length (L) x Height (H) = mm2 or m2 H 2m2

Materials calculations Area - calculations Triangles The area of the triangle is always half the area of a square with the same base and height Area of a triangle = Base x height 2 HEIGHT 2m2 BASE

Materials calculations Formula - triangles Area = ½ Base (B) x Height (H) = mm2 or m2 H 2m2 B

Materials calculations Area if a gable end 4m 3m 6m2 Step 1: Divide up the wall Step 2: Work out the area of each section: 3m x 4m = 12m2 4m x 3m / 2 = 6m2 Step 3: Add the two areas together: 12m2 + 6m2 = 18m2 The area of this gable is 18m2 4m 3m 12m2 4m 3m 18m2

Materials calculations Area - calculations Circles The area of a circle is calculated using  (pi) = 3.14 The formula to find the area of any circle: Area =  x radius x radius The radius (r) is the length from the centre to the edge The diameter (d) is the length from edge to edge, through the centre r d

Materials calculations Formulae - circles Circle Half circle Quarter circle 4m 3m 2m 2m2 The area of this circle is =  x rad x rad = 3.14 x 4 x 4 = 50.24 m2 The area of this half circle is = ( x rad x rad) / 2 = (3.14 x 3 x 3) / 2 = 14.13 m2 The area of this quarter circle is = ( x rad x rad) / 4 = (3.14 x 2 x 2) / 4 = 3.14 m2

Materials calculations Exercise 6m 2.5m 3.2m 4m Area = m2 50.24 Area = m2 113.04 Area = m2 19.625 32.1536 Area = m2 16m 3m 7.4m 14m Area = m2 42.9866 Area = m2 153.86 Area = m2 100.48 Area = m2 7.065

Materials calculations Formula - circles Radius (r) Length from centre to outside edge (mm or m) Diameter (d) Length from edge to edge through centre (mm or m) Circumference (c) Perimeter or edge of circle = 2 r Area  x r x r = r2 (mm2 or m2) c r d 2m2

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