Download - Calculating the Area of Basic Shapes
Construction NumeracyCalculating Areas: Basic Shapes
Stonemasonry Department 2011
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
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
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
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
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
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
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
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
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
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.
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
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
40m²52m²
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
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
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
Class Activity 1 Solution
6m
4m
10m
10m
Area = ½ length x heightArea = 0.5 x 10 x 4Area = 20m²
Area = length x heightArea = 10 x 6 Area = 60m²
Area = length x heightArea = 3.8 x 2.4Area = 9.12m²
Area = length x heightArea = 2.5 x 1.2Area = 3m²
67.88m²
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
Class Activity 2 Solution
9m
6m
16m
16m
Area = ½ length x heightArea = 0.5 x 16 x 6Area = 48m²
Area = length x heightArea = 16 x 9 Area = 144m²
Area = length x heightArea = 3.5 x 2.5Area = 8.75m²
Area = length x heightArea = 2.1 x 1.2Area = 2.52m²
180.73m²
Developed by The Stonemasonry DepartmentCity of Glasgow College
2011