Step-by-Step Learning
Learn about Perimeter and Area through these example problems with detailed step-by-step solutions.
Example 1: Finding the Perimeter of a Rectangle
Calculate the perimeter of a rectangle with length 10 cm and width 6 cm.
Step 1: Recall the formula for the perimeter of a rectangle. The perimeter is the total distance around the outside of the shape.
Step 2: The formula for the perimeter of a rectangle is: Perimeter = $2 \times (\text{Length} + \text{Width})$.
Step 3: Identify the given length and width. Length = 10 cm, Width = 6 cm.
Step 4: Substitute the values into the formula: Perimeter = $2 \times (10 \text{ cm} + 6 \text{ cm})$.
Step 5: First, add the length and width: $10 + 6 = 16$ cm.
Step 6: Now, multiply the sum by 2: Perimeter = $2 \times 16$ cm = 32 cm.
Step 7: Therefore, the perimeter of the rectangle is 32 centimeters.
Example 2: Finding the Area of a Square
Calculate the area of a square with a side length of 7 meters.
Step 1: Recall the formula for the area of a square. The area is the amount of space inside the shape.
Step 2: The formula for the area of a square is: Area = Side Length $\times$ Side Length (or Side Length²).
Step 3: Identify the given side length. Side Length = 7 meters.
Step 4: Substitute the value into the formula: Area = $7 \text{ m} \times 7 \text{ m}$.
Step 5: Multiply the side length by itself: $7 \times 7 = 49$.
Step 6: The unit for area is square units. Since the side length is in meters, the area is in square meters ($m^2$).
Step 7: Therefore, the area of the square is 49 square meters.
Example 3: Word Problem (Perimeter)
A rectangular garden is 15 meters long and 8 meters wide. A fence is to be built around the garden. What is the total length of the fence needed?
Step 1: Understand that building a fence around the garden means finding the perimeter of the rectangular garden.
Step 2: Identify the dimensions of the rectangle: Length = 15 meters, Width = 8 meters.
Step 3: Use the formula for the perimeter of a rectangle: Perimeter = $2 \times (\text{Length} + \text{Width})$.
Step 4: Substitute the values into the formula: Perimeter = $2 \times (15 \text{ m} + 8 \text{ m})$.
Step 5: Add the length and width: $15 + 8 = 23$ meters.
Step 6: Multiply the sum by 2: Perimeter = $2 \times 23$ meters = 46 meters.
Step 7: The total length of the fence needed is 46 meters.
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