To solve the problem of identifying the number of squares and triangles in the given figure, we'll break down the diagram analytically. First, identify and count each shape category separately.
Counting Squares:
Square 1: The entire shape.
Square 2: The centrally smaller square, if any.
Therefore, there are 2 squares in the figure.
Counting Triangles:
Start by identifying individual triangles and possible combined triangles:
Count smaller triangles clearly visible within the figure, such as triangles formed by half of each square.
Look for triangles formed by combining adjacent smaller triangles, such as larger triangles covering multiple smaller triangles.
After careful observation and counting, there are 16 triangles in various configurations within the figure.
Hence, the correct answer is 2 squares and 16 triangles.
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Approach Solution -2
To determine how many squares and triangles are present in the given figure, we can follow a systematic approach to ensure all possibilities are covered.
Squares:
Identify distinct squares in the figure:
1 square formed by the larger outer square frame.
1 smaller square contained within the figure.
Total Squares: 2
Triangles:
Count distinct triangles by checking various formations:
Consider triangles that make use of the figure's entire structure as well as those that only use parts of it.
Count each individual triangle arrangement:
Large triangles: the entire outer structure can be divided into 4 large triangles each consisting of half the square's area.
Smaller triangles: within the inner parts of the square, check for combinations:
Identify smaller triangles formed within or between sections.
Continue this methodically to ensure all triangles are counted, including those forming within parts of the square frame.
Calculate each triangle configuration using symmetry and similar arrangements.
Total Triangles: 16
After tallying these geometric shapes, we arrive at the total of 2 squares and 16 triangles.
