Counting Figures
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Introduction
Counting Figures involves finding the total number of specific geometric shapes (Triangles, Squares, Rectangles, Lines) hidden within a complex figure.
Counting Triangles
1. From Vertex: If a triangle is divided by 'n' vertical lines from a vertex, total triangles = Sum of parts = 1 + 2 + ... + (n+1). Correct Formula: If base is divided into n parts, triangles = n(n+1)/2.
2. In a Box: If a square/rectangle is divided by diagonals into 'n' small triangles, total triangles = 2 ├Ч n.
2. In a Box: If a square/rectangle is divided by diagonals into 'n' small triangles, total triangles = 2 ├Ч n.
Counting Squares & Rectangles
1. Squares in NxN Grid: 1┬▓ + 2┬▓ + ... + N┬▓.
2. Squares in MxN Grid: (M├ЧN) + ((M-1)├Ч(N-1)) + ... until one dimension is 1.
3. Rectangles in NxN Grid: (Sum of 1 to N)┬▓. Or Cube Sum: 1┬│ + 2┬│ + ... + N┬│.
2. Squares in MxN Grid: (M├ЧN) + ((M-1)├Ч(N-1)) + ... until one dimension is 1.
3. Rectangles in NxN Grid: (Sum of 1 to N)┬▓. Or Cube Sum: 1┬│ + 2┬│ + ... + N┬│.
Straight Lines
Count Horizontal (H), Vertical (V), and Slant (S) lines separately. Total = H + V + S.
ЁЯза
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