If the drawing depicts 10 squared, and the face of this shape is 160 cm2, find the perimeter of this shape?

If the drawing depicts "10 squared," which implies a square with a side length of 10 units, and you're told that the face of this shape is 160 cm², then there seems to be some confusion. A square with a side length of 10 cm would actually have an area of \(10 \times 10 = 100\) cm², not 160 cm².

However, let's assume the 160 cm² represents the actual area, and we need to find the perimeter of this square.

1. **Find the side length of the square:**
   \[
   \text{Area} = \text{side}^2
   \]
   \[
   \text{side} = \sqrt{160} = \sqrt{16 \times 10} = 4\sqrt{10} \text{ cm}
   \]

2. **Calculate the perimeter of the square:**
   \[
   \text{Perimeter} = 4 \times \text{side} = 4 \times 4\sqrt{10} = 16\sqrt{10} \text{ cm}
   \]

So, the perimeter of the shape is \(16\sqrt{10}\) cm.

Would you like more details on the steps, or do you have any questions?

Here are some related questions:
1. How would the calculation change if the area were 200 cm²?
2. What is the exact numerical value of \(16\sqrt{10}\) cm?
3. What would the perimeter be if the side length were 12 cm instead?
4. How does the formula for the area of a square relate to its perimeter?
5. What are the units of the perimeter if the area is given in square meters?

**Tip:** When given the area of a square, you can always find the side length by taking the square root of the area.

Learn how to calculate the perimeter of a square with a given area of 160 cm². Understand the relationship between the area and perimeter of a square. Suitable for high school students studying geometry.

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