How many rectangles are there in the given figure?
- A13
- B14
- C15
- D17
Solution & Step-by-step Explanation
Let's count the total number of rectangles systematically by analyzing row components and combined shapes:
1. Count Rectangles Within Row 1 (Top Row):
* Contains 2 small individual rectangles.
* Combining them horizontally creates 1 large rectangle.
* Total in Row 1 = rectangles.
2. Count Rectangles Within Row 2 (Middle Row):
* Contains 3 independent sections (left block, full middle block, right block).
* Combining adjacent blocks: (Left + Middle) = 1, (Middle + Right) = 1.
* Combining all 3 blocks together = 1.
* Total in Row 2 = rectangles.
3. Count Rectangles Within Row 3 (Bottom Row):
* Identical layout to Row 1: contains 2 small individual rectangles.
* Combining them horizontally creates 1 large rectangle.
* Total in Row 3 = rectangles.
4. Count Rectangles Formed By Combining Multiple Rows Vertically:
Due to the staggered brick-wall layout, vertical dividing lines are offset between adjacent rows. This means partial vertical combinations do not form valid straight-edged rectangles unless we take the full width of the block:
* Combining Row 1 + Row 2 across the full width = 1 rectangle.
* Combining Row 2 + Row 3 across the full width = 1 rectangle.
* Combining Row 1 + Row 2 + Row 3 together (the complete outer boundary structure) = 1 rectangle.
Summing up all calculated distinct values:
1. Count Rectangles Within Row 1 (Top Row):
* Contains 2 small individual rectangles.
* Combining them horizontally creates 1 large rectangle.
* Total in Row 1 = rectangles.
2. Count Rectangles Within Row 2 (Middle Row):
* Contains 3 independent sections (left block, full middle block, right block).
* Combining adjacent blocks: (Left + Middle) = 1, (Middle + Right) = 1.
* Combining all 3 blocks together = 1.
* Total in Row 2 = rectangles.
3. Count Rectangles Within Row 3 (Bottom Row):
* Identical layout to Row 1: contains 2 small individual rectangles.
* Combining them horizontally creates 1 large rectangle.
* Total in Row 3 = rectangles.
4. Count Rectangles Formed By Combining Multiple Rows Vertically:
Due to the staggered brick-wall layout, vertical dividing lines are offset between adjacent rows. This means partial vertical combinations do not form valid straight-edged rectangles unless we take the full width of the block:
* Combining Row 1 + Row 2 across the full width = 1 rectangle.
* Combining Row 2 + Row 3 across the full width = 1 rectangle.
* Combining Row 1 + Row 2 + Row 3 together (the complete outer boundary structure) = 1 rectangle.
Summing up all calculated distinct values: