Let us consider a rather routine problem of laying a brick patio. You will use some answers more than once.
Answer (2)
Convert feet to inches: 13 ft = 156 inches , 18 ft = 216 inches .
Calculate total dimensions in inches: width = 162 inches , length = 225 inches .
Determine the number of bricks in the English system: 3.75 × 8 162 × 225 = 1215 bricks .
Determine the number of bricks in the Metric system: 9.5 × 20 400 × 500 ≈ 1053 bricks .
1215 bricks (English) , 1053 bricks (Metric)
Explanation
Problem Overview Let's break down this brick patio problem step-by-step! We'll tackle both the English and Metric systems to figure out how many bricks you'll need.
English System: Converting Feet to Inches First, let's focus on the English system. We need to find the total width and length of the patio in inches. Step 1a involves converting the feet portion of the width and length into inches. Since 1 foot equals 12 inches, we multiply:
Width: 13 ft = 13 × 12 = 156 inches
Length: 18 ft = 18 × 12 = 216 inches
English System: Calculating Total Dimensions Now, in Step 1b, we add these values to the inches already given to find the total width and length:
Total width: 156 inches + 6 inches = 162 inches Total length: 216 inches + 9 inches = 225 inches
English System: Patio Area Next, we calculate the area of the patio in square inches:
Area of patio = width × length = 162 inches × 225 inches = 36450 square inches
English System: Brick Area We also need the area of one brick:
Area of one brick = 3.75 inches × 8 inches = 30 square inches
English System: Number of Bricks To find the number of bricks needed, we divide the total patio area by the area of one brick:
Number of bricks = 30 square inches 36450 square inches = 1215 bricks
Metric System: Converting Meters to Centimeters Now, let's switch to the Metric system. In Step 1a, we convert the width and length from meters to centimeters. Since 1 meter equals 100 centimeters, we multiply:
Width: 4 m = 4 × 100 = 400 cm Length: 5 m = 5 × 100 = 500 cm
Metric System: Patio Area In Step 2, we find the area of the patio in square centimeters:
Area of patio = width × length = 400 cm × 500 cm = 200000 square cm
Metric System: Brick Area The area of one brick is:
Area of one brick = 9.5 cm × 20 cm = 190 square cm
Metric System: Number of Bricks Finally, we calculate the number of bricks needed by dividing the patio area by the brick area:
Number of bricks = 190 square cm 200000 square cm = 1052.63 ≈ 1053 bricks (rounding up since we can't use parts of bricks)
Final Answer So, to cover the patio, you'll need 1215 bricks in the English system and approximately 1053 bricks in the Metric system.
Examples
Imagine you're designing a garden path and need to calculate how many paving stones to purchase. By measuring the path's length and width, and knowing the dimensions of the paving stones, you can use the same area calculation method to determine the exact number of stones required, preventing overspending and ensuring you have enough materials to complete your project. This is a practical application of area calculation in everyday landscaping and construction.
To cover the brick patio, you need about 1215 bricks in the English system and approximately 1053 bricks in the Metric system. This is derived from calculating the area of the patio and the area of a brick. The calculations involve converting measurements to consistent units and using them to find the area and the number of bricks needed.
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