KNOWLEDGE OF QUANTITIES CALCULATING AREAS KNOWLEDGE OF TECHNICAL

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 1 m 2. It is calculated by multiplying the two sides together. It is the space that counts the area, not the shape. 1 m 0. 5 m 4 m 1 m 3 / 0. 25 m 2 m

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 3 m x 4 m = 12 m 2 4 / 5 m x 2 m = 10 m 2 2. 5 m x 4 m = 10 m 2 3. 5 m x 2 m = 7 m 2

MATERIALS CALCULATIONS Take out area Step 1: 3 m Work out the total area: 4 m x 3 m = 12 m 2 Step 2: Work out the area of the opening(s): 2 m x 1 m = 2 m 2 4 m 2 m 2 12 m 2 Step 3: Take the openings from the total area: 12 m 2 – 2 m 2 = 10 m 2 2 m 2 The area of the wall is 10 m 2 5 /

MATERIALS CALCULATIONS Formula - rectangles L Area = Length (L) x Height (H) = mm 2 or m 2 H 2 m 2 6 /

MATERIALS CALCULATIONS Area - calculations Triangles The area of the triangle is always half the area of a square with the same base and height Base x height 2 HEIGHT Area of a triangle = 2 m 2 BASE 7 /

MATERIALS CALCULATIONS Formula - triangles Area = ½ Base (B) x Height (H) = mm 2 or m 2 H 2 m 2 B 8 /

MATERIALS CALCULATIONS Area if a gable end Step 1: Divide up the wall 12 m 2 Step 2: 4 m Work out the area of each section: 3 m x 4 m = 12 m 2 4 m x 3 m / 2 = 6 m 2 3 m 3 m 3 m 4 m Step 3: Add the two areas together: 12 m 2 + 6 m 2 = 18 m 2 3 m The area of this gable is 18 m 2 3 m 4 m 9 / 18 m 2

MATERIALS CALCULATIONS Area - calculations Circles r The area of a circle is calculated using (pi) = 3. 14 The formula to find the area of any circle: Area = 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 10 / d

MATERIALS CALCULATIONS Formulae - circles Circle Half circle Quarter circle 4 m 3 m 2 m 2 m 2 The area of this circle is = x rad = 3. 14 x 4 = 50. 24 m 2 11 / The area of this half circle is = ( x rad) / 2 The area of this quarter circle is = ( x rad) / 4 = (3. 14 x 3) / 2 = 14. 13 m 2 = (3. 14 x 2) / 4 = 3. 14 m 2

MATERIALS CALCULATIONS Exercise 4 m Area = 50. 24 m 2 2. 5 m 6 m Area = 113. 04 m 2 3. 2 m Area = 19. 625 m 2 Area = 32. 1536 m 2 14 m 16 m 3 m 7. 4 m Area = 42. 9866 m 2 12 / Area = 153. 86 m 2 Area = 100. 48 m 2 Area = 7. 065 m 2

MATERIALS CALCULATIONS Formula - circles Radius (r) c Length from centre to outside edge (mm or m) r d Diameter (d) Length from edge to edge through centre (mm or m) Circumference (c) Perimeter or edge of circle = 2 r Area x r = r 2 (mm 2 or m 2) 13 / 2 m 2

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