**Step 1. Understand What "Perimeter" Means**

The perimeter is the total distance around a two-dimensional shape. It is the sum of the lengths of all the sides of the shape.

**Step 2. Identify the Shape**

The formula used to compute the perimeter depends on the shape:

- **For a rectangle** with length \( l \) and width \( w \), the perimeter \( P \) is
  \[
  P = 2(l + w)
  \]
- **For a square** with side length \( s \), the perimeter \( P \) is
  \[
  P = 4s
  \]
- **For a triangle** with side lengths \( a \), \( b \), and \( c \), the perimeter \( P \) is
  \[
  P = a + b + c
  \]
- **For a regular \( n \)-sided polygon** with side length \( s \), the perimeter \( P \) is
  \[
  P = n \times s
  \]

**Step 3. Compute the Perimeter**

To compute the perimeter:

1. Identify the shape.
2. Determine the appropriate formula.
3. Substitute the given dimensions into the formula.
4. Perform the arithmetic to find the result.

For example, if you have a rectangle with \( l = 5 \) and \( w = 3 \), then the perimeter is
\[
P = 2(5 + 3) = 2 \times 8 = 16.
\]

If you have further information or a specific shape and dimensions, please provide them so the calculation can be more precise.

Home Question Bank Math Geometry

Question

Perimeter

Ask by Boone Watson. in the Philippines

Mar 12,2025

Upstudy AI Solution

Tutor-Verified Answer

Answer

To find the perimeter of a shape, add up the lengths of all its sides. For a rectangle, use \( P = 2(l + w) \), where \( l \) is the length and \( w \) is the width. For a square, use \( P = 4s \), where \( s \) is the side length. For a triangle, add all three side lengths together. For a regular polygon with \( n \) sides, use \( P = n \times s \), where \( s \) is the length of one side.

Solution

**Step 1. Understand What "Perimeter" Means** The perimeter is the total distance around a two-dimensional shape. It is the sum of the lengths of all the sides of the shape. **Step 2. Identify the Shape** The formula used to compute the perimeter depends on the shape: - **For a rectangle** with length \( l \) and width \( w \), the perimeter \( P \) is \[ P = 2(l + w) \] - **For a square** with side length \( s \), the perimeter \( P \) is \[ P = 4s \] - **For a triangle** with side lengths \( a \), \( b \), and \( c \), the perimeter \( P \) is \[ P = a + b + c \] - **For a regular \( n \)-sided polygon** with side length \( s \), the perimeter \( P \) is \[ P = n \times s \] **Step 3. Compute the Perimeter** To compute the perimeter: 1. Identify the shape. 2. Determine the appropriate formula. 3. Substitute the given dimensions into the formula. 4. Perform the arithmetic to find the result. For example, if you have a rectangle with \( l = 5 \) and \( w = 3 \), then the perimeter is \[ P = 2(5 + 3) = 2 \times 8 = 16. \] If you have further information or a specific shape and dimensions, please provide them so the calculation can be more precise.

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The Deep Dive

Did you know that the concept of perimeter dates back to ancient civilizations? The early Egyptians and Greeks were already calculating the perimeter of various shapes, particularly in the context of land measurements and construction. For instance, the Greeks used the perimeter in their early studies of geometry, which eventually laid the groundwork for mathematical exploration that still shapes our understanding today! In real-world applications, understanding perimeter is crucial for tasks like landscaping, fencing, and even packaging. When you know the perimeter, you can figure out how much material you need to enclose a garden or build a fence, or determine the right size for making boxes that fit snugly around your products. It’s all about keeping things neat and tidy!

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