The area \(A\) of a rectangle is given by the formula:
\(A = L \times W\)
where \(L\) and \(W\) are the length and width, respectively, of the rectangle.
How to Find the Area of a Rectangle? Examples with Solutions
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Example 1: Find the area of a rectangle of length 35 meters and width 20 meters.
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Since the length \(L\) and the width \(W\) have the same units, we apply the formula by substituting \(L\) and \(W\) with their values:
\(A = L \times W = 35 \times 20 = 700\text{ square meters (or m}^2\text{)}\). -
Example 2: A rectangular field has a length of 360 inches and a width of 300 inches. Find the area of the rectangle in square feet. (1 foot = 12 inches)
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Since we need to find the area in square feet, we first convert the length \(L\) and width \(W\) into feet:
\(L = 360\text{ inches} \div 12 = 30\text{ feet}\)
\(W = 300\text{ inches} \div 12 = 25\text{ feet}\)
The area \(A\) of the rectangle is given by:
\(A = L \times W = 30 \times 25 = 750\text{ square feet (or ft}^2\text{)}\). -
Example 3: The width of a rectangle is 20 meters and its length is five fourths of its width. Find the area of this rectangle.
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We first need to find the length \(L\) of the rectangle given its width \(W = 20\text{ meters}\):
\(L = \left(\dfrac{5}{4}\right) \times W = \left(\dfrac{5}{4}\right) \times 20 = \dfrac{5 \times 20}{4} = 25\text{ meters}\)
The area \(A\) of the rectangle is given by:
\(A = L \times W = 25 \times 20 = 500\text{ square meters (m}^2\text{)}\). -
Example 4: The length of a rectangle is 1200 meters and its width is 100 meters shorter than its length. Find the area of this rectangle in square kilometers. (1 kilometer = 1000 meters)
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We first need to find the width \(W\) of the rectangle given its length \(L = 1200\text{ meters}\):
\(W = 1200 - 100 = 1100\text{ meters}\)
Next, convert the length \(L\) and the width \(W\) into kilometers:
\(L = 1200\text{ meters} \div 1000 = 1.2\text{ kilometers}\)
\(W = 1100\text{ meters} \div 1000 = 1.1\text{ kilometers}\)
The area \(A\) of the rectangle is calculated as follows:
\(A = L \times W = 1.2 \times 1.1 = 1.32\text{ square kilometers (or km}^2\text{)}\). -
Example 5: A rectangular room of length 5 meters and width 4.5 meters is to be tiled with square tiles of 20 cm per side. What is the minimum number of tiles needed?
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Find the area \(A_1\) of one tile in square centimeters:
\(A_1 = 20 \times 20 = 400\text{ square centimeters}\).
Convert the length \(L\) and width \(W\) of the room into centimeters and find its area \(A\):
\(L = 5 \times 100 = 500\text{ centimeters}\)
\(W = 4.5 \times 100 = 450\text{ centimeters}\)
\(A = 500 \times 450 = 225,000\text{ square centimeters}\)
The number \(N\) of tiles needed is given by dividing the total area of the room by the area of one tile:
\(N = \dfrac{\text{Total area of the room}}{\text{Area of one tile}} = \dfrac{225,000}{400} = 562.5\text{ tiles}\)
Since the number of tiles must be an integer, and cutting tiles in practice requires rounding up, the minimum number of tiles needed is 563.