Perimeter for 5th Grade: Find the Distance Around

Perimeter is the distance around the outside of a shape. In Grade 5, students find the perimeter of polygons—triangles, rectangles, squares, and other shapes—by adding the lengths of all sides. Perimeter is used when fencing a garden, framing a picture, running around a track, or measuring the boundary of any region.

For a rectangle, the perimeter is \(2 \times (\text{length} + \text{width})\) because opposite sides are equal. For a square, the perimeter is \(4 \times \text{side}\) because all four sides are equal. For any polygon, the perimeter is the sum of all side lengths.

DETAILED EXPLANATION

Perimeter = sum of all side lengths of a polygon.

Rectangle: \(P = 2l + 2w = 2(l + w)\), where l = length and w = width.

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Square: \(P = 4s\), where s = side length.

Triangle: \(P = a + b + c\), where a, b, c are the three side lengths.

Any polygon: Add the lengths of all sides.

Units: Use the same unit as the side lengths (cm, m, ft, etc.).

WORKED EXAMPLES WITH STEP BY STEP SOLUTIONS

Example 1

A rectangle has length 8 cm and width 5 cm. Find the perimeter.

Solutions:

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Step 1: The perimeter of a rectangle is \(P = 2 \times (\text{length} + \text{width})\).

Step 2: Substitute: \(P = 2 \times (8 + 5) = 2 \times 13 = 26\).

Step 3: The perimeter is 26 cm.

Answer: 26 cm

Example 2

A square has side length 6 m. Find the perimeter.

Solutions:

Step 1: The perimeter of a square is \(P = 4 \times \text{side}\).

Step 2: Substitute: \(P = 4 \times 6 = 24\).

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Step 3: The perimeter is 24 meters.

Answer: 24 meters

Example 3

A triangle has sides 5 cm, 7 cm, and 9 cm. Find the perimeter.

Solutions:

Step 1: For any polygon, perimeter = sum of all side lengths.

Step 2: \(P = 5 + 7 + 9 = 21\).

Step 3: The perimeter is 21 cm.

Answer: 21 cm

Example 4

A pentagon has sides of 3 m, 4 m, 5 m, 4 m, and 3 m. Find the perimeter.

Solutions:

Step 1: Add all five side lengths.

Step 2: \(P = 3 + 4 + 5 + 4 + 3 = 19\).

Answer: 19 m