Problem 102
Question
Will help you prepare for the material covered in the next section. Find the perimeter and the area of each rectangle with the given dimensions: a. 40 yards by 30 yards b. 50 yards by 20 yards.
Step-by-Step Solution
Verified Answer
For rectangle a, the area is 1200 square yards and the perimeter is 140 yards. For rectangle b, the area is 1000 square yards and the perimeter is 140 yards.
1Step 1: Find the Area and Perimeter of the First Rectangle
First, apply the formulas to the first rectangle. The length is 40 yards, and the width is 30 yards. The area is calculated by multiplying the length by the width. So the area is \(40 yards * 30 yards = 1200 square yards\). The perimeter is calculated as twice the sum of the length and the width, so the perimeter is \(2 * (40 yards + 30 yards) = 2 * 70 yards = 140 yards\).
2Step 2: Find the Area and Perimeter of the Second Rectangle
Next, apply these formulas to the second rectangle. The length is 50 yards, and the width is 20 yards. Therefore, the area is \(50 yards * 20 yards = 1000 square yards\). The perimeter for this rectangle is \(2 * (50 yards + 20 yards) = 2 * 70 yards = 140 yards\).
Key Concepts
Area CalculationPerimeter CalculationRectangles
Area Calculation
Calculating the area of a rectangle involves a straightforward formula. The area represents the amount of space within the rectangle's boundaries. Imagine filling the rectangle with unit squares, and you'll get the idea that area measures how many of these squares fit inside.
To find the area, you use the formula:
\[ \text{Area} = 40 \, \text{yards} \times 30 \, \text{yards} = 1200 \, \text{square yards} \]
Similarly, for another rectangle measuring 50 yards in length and 20 yards in width, the area calculation would be:
\[ \text{Area} = 50 \, \text{yards} \times 20 \, \text{yards} = 1000 \, \text{square yards} \]
Always remember, the area is expressed in square units.
To find the area, you use the formula:
- Area = Length × Width.
\[ \text{Area} = 40 \, \text{yards} \times 30 \, \text{yards} = 1200 \, \text{square yards} \]
Similarly, for another rectangle measuring 50 yards in length and 20 yards in width, the area calculation would be:
\[ \text{Area} = 50 \, \text{yards} \times 20 \, \text{yards} = 1000 \, \text{square yards} \]
Always remember, the area is expressed in square units.
Perimeter Calculation
The perimeter of a rectangle is essentially the total length of its outer boundary. Imagine walking along the edges of the rectangle – this length is the perimeter.
The formula to calculate the perimeter of a rectangle is:
As an example, for a rectangle with a length of 40 yards and a width of 30 yards, the perimeter is calculated as:
\[ \text{Perimeter} = 2 \times (40 \, \text{yards} + 30 \, \text{yards}) = 2 \times 70 \, \text{yards} = 140 \, \text{yards} \]
Similarly, for a rectangle measuring 50 yards in length and 20 yards in width:
\[ \text{Perimeter} = 2 \times (50 \, \text{yards} + 20 \, \text{yards}) = 2 \times 70 \, \text{yards} = 140 \, \text{yards} \]
This calculation helps in understanding the complete boundary distance.
The formula to calculate the perimeter of a rectangle is:
- Perimeter = 2 × (Length + Width).
As an example, for a rectangle with a length of 40 yards and a width of 30 yards, the perimeter is calculated as:
\[ \text{Perimeter} = 2 \times (40 \, \text{yards} + 30 \, \text{yards}) = 2 \times 70 \, \text{yards} = 140 \, \text{yards} \]
Similarly, for a rectangle measuring 50 yards in length and 20 yards in width:
\[ \text{Perimeter} = 2 \times (50 \, \text{yards} + 20 \, \text{yards}) = 2 \times 70 \, \text{yards} = 140 \, \text{yards} \]
This calculation helps in understanding the complete boundary distance.
Rectangles
A rectangle is a four-sided figure, with opposite sides that are equal in length and all angles being right angles (90 degrees). It’s one of the most common shapes encountered in geometry.
Rectangles hold significance in both mathematical theory and practical applications. Whether it’s the design of rooms, gardens, or screens, recognizing their properties helps us work effectively with them.
Understanding these properties aids in solving problems related to area and perimeter.
The symmetry and simplicity of rectangles make them easier tools for calculation, design, and understanding the basic principles of geometry.
Rectangles hold significance in both mathematical theory and practical applications. Whether it’s the design of rooms, gardens, or screens, recognizing their properties helps us work effectively with them.
- Properties of a rectangle include:
- Opposite sides are equal.
- All angles are 90 degrees.
- Diagonals are equal.
Understanding these properties aids in solving problems related to area and perimeter.
The symmetry and simplicity of rectangles make them easier tools for calculation, design, and understanding the basic principles of geometry.
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