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

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. 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. 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. 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. 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. 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. 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. 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. 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. 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
3m
12m²
5m 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. Surface Area of a Gable
3m
12m²
5m 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. Surface Area of a Gable
3m
2m²
5m
6m²
8m
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

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 of
the openings to obtain the area of masonry walling required to build the
gable.

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. Class Activity 1 Solution
Area = ½ length x height
4m Area = 0.5 x 10 x 4
Area = 20m²
10m
Area = length x height
Area = 10 x 6
Area = 60m²
6m
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. 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. Class Activity 2 Solution
Area = ½ length x height
6m Area = 0.5 x 16 x 6
Area = 48m²
16m
Area = length x height
Area = 16 x 9
Area = 144m²
9m
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. Developed by The Stonemasonry Department
City of Glasgow College
2011