Counting Figures
Counting figures is a core part of the General Intelligence and Reasoning section in competitive exams. In this topic, students must find the total number of specific geometric shapes within a complex diagram. These shapes usually include triangles, squares, rectangles, or circles. It is not just about looking at the picture. It is about using a logical and systematic method. This ensures no shape is missed or counted twice. This skill is vital because it tests your spatial visualization.
Concepts (3)
To count squares in a grid where the number of rows and columns are the same, we use the square sum method. If the grid is 3 by 3, you take the number of rows (3) and square every number down to 1. So, you add 3 squared, 2 squared, and 1 squared.
To count squares in a grid where the number of rows and columns are the same, we use the square sum method. If the grid is 3 by 3, you take the number of rows (3) and square every number down to 1. So, you add 3 squared, 2 squared, and 1 squared. This gives 9 + 4 + 1 = 14 squares. This counts the tiny squares and the larger blocks together.
When a large triangle is divided into smaller parts by lines from the top point to the base, we use a simple addition rule. First, number each small base segment as 1, 2, 3, and so on. The total number of triangles is the sum of these numbers.
When a large triangle is divided into smaller parts by lines from the top point to the base, we use a simple addition rule. First, number each small base segment as 1, 2, 3, and so on. The total number of triangles is the sum of these numbers. For example, if there are 3 segments, the total triangles will be 1 + 2 + 3 = 6. This counts the 3 small triangles, 2 medium ones, and 1 large triangle.
Counting rectangles is different from counting squares. You must sum the numbers of the rows and the numbers of the columns separately. Then, multiply these two sums together. For example, in a grid with 2 rows and 3 columns, the row sum is 1+2=3.
Counting rectangles is different from counting squares. You must sum the numbers of the rows and the numbers of the columns separately. Then, multiply these two sums together. For example, in a grid with 2 rows and 3 columns, the row sum is 1+2=3. The column sum is 1+2+3=6. The total number of rectangles is 3 multiplied by 6, which equals 18.
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Start Lesson: Squares in a Square Grid