How many rectangles are there in the given figure?
Correct Answer:
B. 30
Explanation:
To determine the total number of rectangles in a grid-like figure, you can use a systematic counting method or a combinatorial formula. Since every square is also a rectangle, the goal is to count all possible four-sided shapes with 90-degree angles. Method 1: Manual Counting by Size1. Identify the smallest units: Count all individual 1x1 squares. 2. Form larger shapes: Group adjacent squares to form 1x2, 2x1, 2x2, and larger combinations. 3. Sum the totals: Add the counts from each size category to find the final number.Method 2: Combinatorial Formula A rectangle is defined by choosing two horizontal lines and two vertical lines from the grid.1. Count the number of horizontal lines (h) and vertical lines (v). 2. Use the formula: (hC2) x (vC2). 3. This calculation—\[h(h-1)/2\] multiplied by \[v(v-1)/2\]—provides the total number of rectangles instantly.For a standard grid with 3 horizontal and 4 vertical lines, the calculation would be 3 x 6 = 18. If the figure is irregular, manual counting by labeling segments is the most accurate approach to ensure no overlaps are missed.
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