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.



6m

6m


Area = 6 x 6

Area = 36m²

7m

7m


Area = 7 x 7

Area = 49m²


3m

3m


Area = 3 x 3

Area = 9m²

9.4m

9.4m


Area = 9.4 x 9.4

Area = 88.36m²

Surface Area of a Rectangle

6m

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.



8m

6m


Area = 8 x 6

Area = 48m²

9m

8m


Area = 9 x 8

Area = 72m²


3m

2m


Area = 3 x 2

Area = 6m²

5.2m

3.9m


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


6m

6m

Area = ½ x Length x Height

Area = 0.5 x 6 x 6

Area = 18m²

3m

5m


Area = 0.5 x 3 x 5

Area = 7.5m²


5m

8.4m


Area = 0.5 x 5 x 8.4

Area = 21m²

0.46m

1.2m


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.


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


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


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


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



180.73m²

Developed by The Stonemasonry DepartmentCity of Glasgow College

2011

calculating the area of basic shapes

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