The diagram shows a figure that contains 7 identical squares. The area of the figure is 112 cm². Find its perimeter.
A) 48 cm
B) 52 cm
C) 54 cm
D) 56 cm
Find the perimeter of the figure containing 7 identical squares whose total area is 112 cm².
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To find the perimeter of the figure made of 7 identical squares, we first calculate the area of one square. Since the total area is 112 cm² and there are 7 squares:
Area of one square = Total area / Number of squares = 112 cm² / 7 = 16 cm².
Next, we find the side length of one square by taking the square root of the area:
Side length = √16 cm² = 4 cm.
Now, we need to understand the arrangement of the squares to compute the perimeter. Depending on the layout, let’s assume they are arranged to form a larger rectangle.
Typically, arrangements like a 3×2 grid of squares, where two squares are stacked vertically, would give a perimeter calculation like this:
Length = 3 squares * 4 cm = 12 cm
Width = 2 squares * 4 cm = 8 cm
Perimeter = 2*(Length + Width) = 2*(12 cm + 8 cm) = 2*20 cm = 40 cm.
However, with 7 squares, one possible compact arrangement could extend that perimeter further, for instance:
If you visualize other shapes or arrangements, but typically keeping overlaps in mind adjusts that perimeter significantly. Checking through basic perimeter calculations leads us to find the area and perimeter can adjust based on arrangement.
With some arrangements, the highest possible perimeter, considering overlaps or shapes utilized would yield:
Final calculation: A common perimeter adjustment based