To find the perimeter and area of the plus-shaped polygon, we need to analyze the given information.
Dimensions:
- The squares have sides of 2 inches.
- The rectangle has a width of 2 inches and a length of 6 inches.
Shape Description:
The plus-shaped polygon consists of:
- A rectangle that is 2 inches wide and 6 inches long.
- A square on the top, centered at the top side of the rectangle.
- A square on the bottom, centered at the bottom side of the rectangle.
1. Calculating the Perimeter:
To find the perimeter, we need to add up all the outer sides of the plus-shaped figure.
- The sides of the rectangle can be categorized as follows:
- The left and right sides of the rectangle: Since the rectangle is 2 inches wide, both sides contribute 2 inches each. Thus, the contribution from the two sides is \(2 + 2 = 4\) inches.
- The top and bottom sides of the rectangle are 6 inches each, but since they are shared with the squares on top and bottom, we need to count only the segments that are outside the squares.
The squares have sides of 2 inches, so the contribution from the top and bottom sides is:
- For the top side: we take the outer segments of the rectangle (left portion of rectangle + width of square on the right):
- Left horizontal segment of rectangle: 2 inches
- Width of square: 2 inches
- Right horizontal segment of rectangle (it is flushed with the square): 2 inches
Total from the top side = \(2 + 2 = 4\) inches (both parts are contributing as squares overlap with the rectangle)
The same calculation applies to the bottom side which contributes another 4 inches.
So the total perimeter can be calculated as: \[ P = (2 + 2) + (2 + 2 + 2 + 2) + (2 + 2) = 4 + 4 + 4 = 12 \text{ inches} \]
2. Calculating the Area:
To find the area, we can separately calculate the area of the rectangle and the area of the two squares, then sum them up.
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Area of the Rectangle: \[ \text{Area of rectangle} = \text{width} \times \text{length} = 2 \times 6 = 12 \text{ square inches} \]
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Area of Each Square: \[ \text{Area of each square} = \text{side} \times \text{side} = 2 \times 2 = 4 \text{ square inches} \] Since there are two squares, we get: \[ \text{Total area from squares} = 2 \times 4 = 8 \text{ square inches} \]
Total Area Calculation:
\[ \text{Total Area} = \text{Area of rectangle} + \text{Total area from squares} = 12 + 8 = 20 \text{ square inches} \]
Conclusion:
- Perimeter: \(12\) inches
- Area: \(20\) square inches
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