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    Calculating the Perimeter of Kite Wxyz

    yunBy Updated:No Comments3 Mins Read
    Calculating the Perimeter of Kite Wxyz

    A kite is a type of quadrilateral with two distinct pairs of adjacent sides that are equal in length. This unique geometric shape often prompts questions about its properties and measurements, particularly its perimeter. Understanding how to calculate the perimeter of a kite involves knowing the lengths of its sides and applying basic arithmetic. This article will guide you through the process of calculating the perimeter of kite WXYZ.

    Properties of a Kite

    Definition

    A kite is a quadrilateral with the following properties:

    • Two pairs of adjacent sides are of equal length.
    • One pair of opposite angles (where the unequal sides meet) are equal.
    • The diagonals intersect at right angles, with one of the diagonals bisecting the other.

    Labeling Kite WXYZ

    For kite WXYZ:

    • WX and XY are one pair of equal adjacent sides.
    • YZ and ZW are the other pair of equal adjacent sides.

    Calculating the Perimeter

    Formula for the Perimeter

    The perimeter of a kite is the sum of the lengths of all its sides. Given that a kite has two pairs of equal sides, the formula can be simplified as: Perimeter=2×(length of one pair of equal sides)+2×(length of the other pair of equal sides)\text{Perimeter} = 2 \times (\text{length of one pair of equal sides}) + 2 \times (\text{length of the other pair of equal sides})Perimeter=2×(length of one pair of equal sides)+2×(length of the other pair of equal sides)

    Steps to Calculate

    1. Identify the Lengths of the Sides:
      • Let aaa be the length of sides WX and XY.
      • Let bbb be the length of sides YZ and ZW.
    2. Apply the Perimeter Formula: Perimeter=2a+2b\text{Perimeter} = 2a + 2bPerimeter=2a+2b

    Example Calculation

    Suppose the lengths of the sides of kite WXYZ are:

    • WX = XY = 5 cm
    • YZ = ZW = 7 cm

    Using the formula: Perimeter=2×5 cm+2×7 cm\text{Perimeter} = 2 \times 5 \text{ cm} + 2 \times 7 \text{ cm}Perimeter=2×5 cm+2×7 cm Perimeter=10 cm+14 cm\text{Perimeter} = 10 \text{ cm} + 14 \text{ cm}Perimeter=10 cm+14 cm Perimeter=24 cm\text{Perimeter} = 24 \text{ cm}Perimeter=24 cm

    Thus, the perimeter of kite WXYZ is 24 cm.

    Conclusion

    Calculating the perimeter of a kite like WXYZ is straightforward once you know the lengths of its sides. By recognizing that a kite has two pairs of equal adjacent sides, you can use the simple formula 2a+2b2a + 2b2a+2b to find the perimeter. This method not only provides a quick solution but also enhances your understanding of the geometric properties of kites.

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