Geometry: Area of a Rectangle
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Questions and Answers

What is the formula used to find the width of a rectangle given its diagonal?

  • Width = Diagonal / √2
  • Width = Diagonal - Length
  • Width = Diagonal × √2
  • Width = √(Diagonal^2 - Length^2) (correct)

    • What is the purpose of finding the length of a rectangle given its diagonal and width?

  • To find the perimeter of the rectangle
  • To find the width of the rectangle
  • To find the area of the rectangle (correct)
  • To find the diagonal of the rectangle

    • In the example of the stone slab path, what is the area of each slab?

  • 800 cm squared
  • 1000 cm squared
  • 400 cm squared
  • 600 cm squared (correct)

    • Why are formulas for finding the area of a rectangle useful in real-world applications?

    <p>For both designing a building and landscaping</p> Signup and view all the answers

    What is the unit of measurement for the area of the path in the stone slab example?

    <p>Meters squared</p> Signup and view all the answers

    What is the next step after finding the area of the path in centimeters squared?

    <p>Divide the area of the path by the area of a slab</p> Signup and view all the answers

    What is the final answer in the stone slab example?

    <p>20 slabs will be required</p> Signup and view all the answers

    What is the purpose of finding the length of a rectangle given its diagonal and width in the example?

    <p>To find the area of the rectangle</p> Signup and view all the answers

    What is the advantage of using formulas to find the area of a rectangle?

    <p>All of the above</p> Signup and view all the answers

    What is the first step in finding the number of slabs required to fill the pathway?

    <p>Find the area of the pathway</p> Signup and view all the answers

    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.

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