**Counting Figures**

The theory of counting the figure is based on the study to decrease the time taken to solve the problem. Many mathematicians have provided the basic concept to solve the problem based on the counting of the numbers.

The assignment is based on the counting of the figures. This assignment discussed the different basic knowledge to solve the problem based on the counting of the figure. The question is based on the counting of the figure such as counting of the triangle, rectangle, and square.

In the counting of the figure, different shapes of the figures are provided however they have to count the particular shaped figure. The counting of these shapes involves the basic concept that should be cleared to count exactly the numbers of the shape provided in the figure. The counting of the figure is based on the non-verbal reigning part.

There are three types of questions asked in the counting of the figure.

**Triangles**

In such types of questions, the students have to count the numbers of the triangles in the provided block. The question can be varied according to the examiner however; the counting of the triangles may be one equilateral triangle.

**Rectangles**

In this type of question, the students have to count the numbers of the rectangles in the given block. In any shape, they make many shapes of the triangle or rectangle with coinciding each other. Then the students have to count the numbers of the rectangle in the figure. However, they have to also focus that they have to count the numbers of squares present in the block. All the squares are rectangles but all squares are not rectangles. Therefore, in the counting of the rectangle, the students have to count the numbers of the square present in the figure or block.

**Squares**

The third type of question is asked in the counting of the figure is based on the counting of the square in the given block. To such types of the question, they to find the finds that interaction of four points, by using those points they can count the numbers of the square present in the block.

**How to solve Counting Figures of Triangles?**

The numbers of the triangle formed in the block are 6. The numbers of the triangle formed in the figure can be defined as n (n+1)/2. N is the number of the triangle formed in the figure. In the above figure, 6 blocks of the triangle are formed in the figure. The total number of the triangle is formed in the figure is 6*7/2 equals 21. The total number of triangles formed in the figure is 21. Let’s understand this by the above examples, in the above figure 6+5+4+3+2+1 = 21. The counting of the figure is based on the addition of the different blocks of the triangle. The addition of the sequence series is to count the numbers of the triangles that form the “arithmetic progression”. The sum of the AP is denoted as n*(n+1) /2, in the counting of the figure the AP sequence is formed. Therefore the formula of the AP series is used in the counting of the total number of figures in the given figure.

**How to solve Counting Figures?**

In the solution of counting the figure, the students have to notice the shape of the figure to be counted. They have to start the counting of the figure from the big one means they have to start their counting from the big figure in the block. Then they start to count according to the sequence that therefore they can count the right no of the different shapes asked in the question. In the square, if both diagonals are made in the figure then the number of the triangle formed in the figure can be calculated. First of all the students have to start from the midpoint of the diagonal then start counting from the midpoint and numbering all sides of the points to provide the total numbers of the triangle formed in the square. This rule is also applicable in the rectangle, as all the squares are rectangles. Let’s take another example to count the numbers of the square in the big square. The line from the midpoint is drawn to the opposite side of the square. Then, learners can use similar tricks like counting the triangle in the square, they have to start the counting of the figure from the midpoint inside the big point can give four numbers of the square formed in the big square.

**Conclusion **

In the assignment of the counting of the figure, there is an example provided to count the numbers of the triangle present in the rectangle. Firstly the learner has counted the triangles formed interaction of the diagonals in the rectangles. The total number of triangles formed in the rectangles after the interaction of the diagonals is four. Then the one of the diagonals is erased, and then they found there are two triangles formed in the rectangle similarly with the other side of the triangles. The concept also helps to solve the question based on the counting of the square. There are other examples explained in the above assignments that are based on the counting of the triangle. In the counting of the rectangle, the students have to count the numbers of the square present in the figure or block.