1. How to count the number of figures?
In 11 Plus exams, you will be given a shape or a figure, where you will be asked to identify the shape and count the number of times it is present in the given shape or figure. Let us now learn how to count the number of shapes given in the figure using a simple method.
1.1 Counting number of triangles with solved example
Example: Count the number of triangles in the following figure.
Solution: The first step is to visualise the triangles and try to split them on the basis of the size of the triangles.
In the given shape, we can split the triangles present in the shape into small-sized, medium-sized and large-sized triangles and count the number of each type of triangle separately.
Small-sized triangles:
The brown-cloured triangles shown above are small-sized. There are 10 small-sized triangles in the above figure.
Medium-sized triangles:
The blue-coloured triangles shown above are medium-sized. There are 6 small-sized triangles as shown above in the given figure.
Large-sized triangles:
The green-coloured triangles shown above are large-sized triangles. There are 2 large-sized triangles in the given figure.
The given figure has 8 small-sized triangles, 6 medium-sized triangles, and 2 large-sized triangles.
Total number of triangles present in the given figure = 10+6+2 = 18.
1.2 Counting number of squares with solved example
Example: Count the number of squares present in the figure below.
Solution: Using the similar method as used for counting triangles, let us work out the number of squares in the above figure by splitting it according to size.
Small-sized squares
The brown coloured squares are the smallest squares in the given figure. There are 4 small-sized squares.
Medium-sized squares
The blue-coloured squares are the medium-sized squares in the given figure. There are 5 medium-sized squares.
Large-sized squares
The green-coloured squares are the large-sized squares in the given figure. There are 4 large-sized squares.
Outer squares: Don’t forget to count the outer squares. There are two outer squares present in the given figure as shown below.
The given figure has 4 small-sized squares, 5 medium-sized squares, 4 large-sized squares, and two outer squares.
Total number of squares present in the given figure = 4+5+4+2=15.
