Question

Count the number of triangles and squares in the given figure.

 

• A. 21 triangles, 7 squares
• B. 18 triangles, 8 squares
• C. 20 triangles, 8 squares
• D. 22 triangles, 7 squares

Hint:

When counting geometric figures in puzzles, break down the figure into smaller sections and count individual shapes within those sections. Don't forget to include overlapping or combined shapes.

Answer 1

The Correct Option is A

Step 1: Count the triangles. - The figure consists of several small triangles within larger triangles. - There are 6 small triangles in the bottom layer, 3 triangles in the middle, and 2 triangles at the top of the pyramid. - Additionally, there are 10 triangles formed by combining different segments, including the larger triangles and overlapping areas. Thus, the total number of triangles is: \[ 6 + 3 + 2 + 10 = 21. \] Step 2: Count the squares. - The squares are present in the middle portion of the figure, formed by intersections of lines. - There are 7 squares in total. Thus, the total number of squares is: \[ \boxed{7}. \] Step 3: Final Answer. The figure contains 21 triangles and 7 squares. \[ \boxed{21\ \text{triangles},\ 7\ \text{squares}} \]