Questions and Answers
What is the formula used to find the width of a rectangle given its diagonal?
What is the purpose of finding the length of a rectangle given its diagonal and width?
In the example of the stone slab path, what is the area of each slab?
Why are formulas for finding the area of a rectangle useful in real-world applications?
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What is the unit of measurement for the area of the path in the stone slab example?
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What is the next step after finding the area of the path in centimeters squared?
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What is the final answer in the stone slab example?
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What is the purpose of finding the length of a rectangle given its diagonal and width in the example?
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What is the advantage of using formulas to find the area of a rectangle?
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What is the first step in finding the number of slabs required to fill the pathway?
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Study Notes
Definition of Area
- Area is the measurement of a two-dimensional boundary, such as a piece of land or a drawing of an enclosed shape.
- It is measured in square units only, such as square centimeters.
Characteristics of a Rectangle
- A rectangle is a four-sided, two-dimensional shape with opposite sides equal.
- The corners of a rectangle are equal and 90 degrees.
- A rectangle is a quadrilateral and a parallelogram.
- Diagonal lines spanning opposite corners of a rectangle bisect each other, and the length of both diagonals are the same.
Formula for the Area of a Rectangle
- The area of a rectangle is calculated using the length and width of the rectangle.
- The formula is: Area = Length × Width
- The length is the longest dimensional region, and the width is the smallest dimensional region.
Finding the Area of a Rectangle
- The area can be found by counting the number of squares in the rectangle.
- If the perimeter and length or width are given, the area can be calculated using the formulas.
- If the diagonal and length or width are given, the area can be calculated using the formulas.
Perimeter of a Rectangle
- The perimeter of a rectangle is the sum of all its sides.
- The formula is: Perimeter = 2(Length + Width)
Finding the Area from Perimeter and Length or Width
- If the perimeter and width are given, the length can be calculated using the formula: Length = (Perimeter - 2 × Width) / 2
- If the perimeter and length are given, the width can be calculated using the formula: Width = (Perimeter - 2 × Length) / 2
Finding the Area from Diagonal and Length or Width
- The diagonal of a rectangle divides it into two equivalent right-angled triangles.
- The formula for the diagonal is: Diagonal = √(Length² + Width²)
- If the diagonal and width are given, the length can be calculated using the formula: Length = √(Diagonal² - Width²)
- If the diagonal and length are given, the width can be calculated using the formula: Width = √(Diagonal² - Length²)
Real-World Applications
- Formulas for finding the area of a rectangle can be used in designing a building, carpeting a room, or landscaping.
- Example: calculating the number of stone slabs required to lay a path of a certain length and width.
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Description
Learn how to calculate the area of a rectangle, a four-sided shape with equal opposite sides and right-angled corners. Understand the formula and units of measurement.