Calculating the Area of Basic Shapes

1. Construction Numeracy Calculating Areas: Basic Shapes Stonemasonry Department 2011

2. Surface Area of a Square 4m 4m Area = Length x Height 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. Surface Area of a Square 6m 6m Area = Length x Height Area = 6 x 6 Area = 36m² 7m 7m Area = Length x Height Area = 7 x 7 Area = 49m²

4. Surface Area of a Square 3m 3m Area = Length x Height Area = 3 x 3 Area = 9m² 9.4m 9.4m Area = Length x Height Area = 9.4 x 9.4 Area = 88.36m²

5. Surface Area of a Rectangle 6m 4m Area = Length x Height 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. Surface Area of a Rectangle 8m 6m Area = Length x Height Area = 8 x 6 Area = 48m² 9m 8m Area = Length x Height Area = 9 x 8 Area = 72m²

7. Surface Area of a Rectangle 3m 2m Area = Length x Height Area = 3 x 2 Area = 6m² 5.2m 3.9m Area = Length x Height Area = 5.2 x 3.9 Area = 20.28m²

8. Surface Area of a Triangle 6m 4m Area = ½ Length x Height Area = 0.5 x 6 x 4 Area = 12m² 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. Surface Area of a Triangle 6m 6m Area = ½ x Length x Height Area = 0.5 x 6 x 6 Area = 18m² 3m 5m Area = ½ x Length x Height Area = 0.5 x 3 x 5 Area = 7.5m²

10. Surface Area of a Triangle 5m 8.4m Area = ½ x Length x Height Area = 0.5 x 5 x 8.4 Area = 21m² 0.46m 1.2m Area = ½ x Length x Height Area = 0.5 x 0.46 x 1.2 Area = 0.276m²

11. Surface Area of a Gable The surface areas we need to calculate in stonemasonry are often made up 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. Surface Area of a Gable 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. 5m 3m 8m 12m² 40m²

13. Surface Area of a Gable By adding the areas of the triangular and rectangular sections of the gable we can calculate the total surface area of the gable. 5m 3m 8m 12m² 40m² 52m²

14. Surface Area of a Gable Next 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 5m 3m 8m 2m² 6m²

15. Surface Area of a Gable Finally we take the total surface area and subtract the surface area of the openings to obtain the area of masonry walling required to build the gable. Total Surface Area = 52m² Window Opening = 2m² Door Opening = 6m² Area of Masonry Walling = 44m²

16. Class Activity 1 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. Window Opening = 2.5m x 1.2m Door Opening = 3.8m x 2.4m 6m 4m 10m

17. Class Activity 1 Solution 6m 4m 10m 10m Area = ½ length x height Area = 0.5 x 10 x 4 Area = 20m² Area = length x height Area = 10 x 6 Area = 60m² Area = length x height Area = 3.8 x 2.4 Area = 9.12m² Area = length x height Area = 2.5 x 1.2 Area = 3m² 67.88m²

18. Class Activity 2 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. Window Opening = 2.1m x 1.2m Door Opening = 3.5m x 2.5m 9m 6m 16m

19. Class Activity 2 Solution 9m 6m 16m 16m Area = ½ length x height Area = 0.5 x 16 x 6 Area = 48m² Area = length x height Area = 16 x 9 Area = 144m² Area = length x height Area = 3.5 x 2.5 Area = 8.75m² Area = length x height Area = 2.1 x 1.2 Area = 2.52m² 180.73m²

20. Developed by The Stonemasonry Department City of Glasgow College 2011