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# Calculating the Area of Basic Shapes

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### Calculating the Area of Basic Shapes

1. 1. Construction NumeracyCalculating Areas: Basic Shapes Stonemasonry Department 2011
2. 2. Surface Area of a Square 4m Area = Length x Height 4m Area = 4 x 4 Area = 16m² To calculate the area of a square we multiply the length of the square by the height of the square. Try to use this formula to calculate the area of the square shown above. Area = Length x Height
3. 3. Surface Area of a Square 6m Area = Length x Height 6m Area = 6 x 6 Area = 36m² 7m Area = Length x Height 7m Area = 7 x 7 Area = 49m²
4. 4. Surface Area of a Square 3m Area = Length x Height 3m Area = 3 x 3 Area = 9m² 9.4m Area = Length x Height 9.4m Area = 9.4 x 9.4 Area = 88.36m²
5. 5. Surface Area of a Rectangle 6m Area = Length x Height 4m Area = 6 x 4 Area = 24m² To calculate the area of a rectangle we multiply the length of the rectangle by the height of the rectangle. Try to use this formula to calculate the area of the rectangle shown above. Area = Length x Height
6. 6. Surface Area of a Rectangle 8m Area = Length x Height 6m Area = 8 x 6 Area = 48m² 9m Area = Length x Height 8m Area = 9 x 8 Area = 72m²
7. 7. Surface Area of a Rectangle 3m Area = Length x Height 2m Area = 3 x 2 Area = 6m² 5.2m Area = Length x Height 3.9m Area = 5.2 x 3.9 Area = 20.28m²
8. 8. Surface Area of a Triangle Area = ½ Length x Height 4m Area = 0.5 x 6 x 4 Area = 12m² 6m To calculate the area of a triangle we multiply half the length of the triangle by the height of the triangle. Try to use this formula to calculate the area of the triangle shown above. Area = ½ Length x Height
9. 9. Surface Area of a Triangle Area = ½ x Length x Height 6m Area = 0.5 x 6 x 6 6m Area = 18m² Area = ½ x Length x Height 5m Area = 0.5 x 3 x 5 Area = 7.5m² 3m
10. 10. Surface Area of a Triangle Area = ½ x Length x Height 8.4m Area = 0.5 x 5 x 8.4 5m Area = 21m² Area = ½ x Length x Height 1.2m Area = 0.5 x 0.46 x 1.2 Area = 0.276m² 0.46m
11. 11. Surface Area of a GableThe surface areas we need to calculate in stonemasonry are often madeup of a combination of squares, rectangles and triangles. The image on the left shows a gable end and the image on the right shows how we can depict the gable end using simple shapes.
12. 12. Surface Area of a Gable3m 12m²5m 40m² 8m The first thing we do is to calculate the total surface area which can be achieved by splitting the gable into a square and a triangle.
13. 13. Surface Area of a Gable3m 12m²5m 40m² 52m² 8m By adding the areas of the triangular and rectangular sections of the gable we can calculate the total surface area of the gable.
14. 14. Surface Area of a Gable3m 2m²5m 6m² 8mNext we consider the surface areas of the door and window openings.Lets say the window measures 2m in length and 1m in height and the door opening measures 3m in length and 2 m in height
15. 15. Surface Area of a Gable Total Surface Area = 52m² Window Opening = 2m² Door Opening = 6m² Area of Masonry Walling = 44m² Finally we take the total surface area and subtract the surface area ofthe openings to obtain the area of masonry walling required to build the gable.
16. 16. Class Activity 1 4m Window Opening = 2.5m x 1.2m 6m Door Opening = 3.8m x 2.4m 10m Calculate the surface area of masonry walling required to build the gable shown in the image above. This calculation follows the same processes as the previous calculations.
17. 17. Class Activity 1 Solution Area = ½ length x height4m Area = 0.5 x 10 x 4 Area = 20m² 10m Area = length x height Area = 10 x 6 Area = 60m²6m Area = length x height Area = 2.5 x 1.2 10m Area = 3m² Area = length x height 67.88m² Area = 3.8 x 2.4 Area = 9.12m²
18. 18. Class Activity 2 6m Window Opening = 2.1m x 1.2m 9m Door Opening = 3.5m x 2.5m 16m Calculate the surface area of masonry walling required to build the gable shown in the image above. This calculation follows the same processes as the previous calculations.
19. 19. Class Activity 2 Solution Area = ½ length x height6m Area = 0.5 x 16 x 6 Area = 48m² 16m Area = length x height Area = 16 x 9 Area = 144m²9m Area = length x height Area = 2.1 x 1.2 16m Area = 2.52m² Area = length x height 180.73m² Area = 3.5 x 2.5 Area = 8.75m²
20. 20. Developed by The Stonemasonry Department City of Glasgow College 2011