how to derive the formula of area of rhombus​

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how to derive the formula of area of rhombus​

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Gabriella 3 months 2021-11-02T19:16:57+00:00 2 Answers 0 views 0

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    0
    2021-11-02T19:18:12+00:00

    ANSWER:-

    DIFF. FORMULAS TO FIND THE AREA OF RHOMBUS ARE:

    formulas to calculate area of rhombus

    using \: diagonals \:  \:  \:  \:  \: a =  \frac{1}{2} \times  d_{1} \times  d_{2}

    using \: base \: and \: height \:  \:  \:  \:   a  = b \times h

    using \: trignometry \:  \:  \:  \:  a =  {b}^{2}  \times  \sin(a)

    where

     d_{1} = length \: of \: diagonal \: 1

    d_{2} = length \: of \: diagonal \: 2

    b= length \: of \: any \: side

    h = height \: of \: rhombus

    a = measure \: of \: any \: interior \: angle

    DERIVATION OF FORMULA:-

    The Area of the rhombus will be:

    A = 4 × area of ∆ AOB

    = 4 × (½) × AO × OB sq. units

    = 4 × (½) × (½) d1 × (½) d2 sq. units

    = 4 × (1/8) d1 × d2 square units

    = ½ × d1 × d2

    Therefore, Area of a Rhombus = A = ½ × d1 × d2

    Where d1 and d2 are the diagonals of the rhombus.

    Hope it’s clarify u

    have a great day ❣️

    0
    2021-11-02T19:18:16+00:00

    \huge\pink{ANSWER:-}

    DIFF. FORMULAS TO FIND THE AREA OF RHOMBUS ARE:

    formulas to calculate area of rhombus

    using \: diagonals \:  \:  \:  \:  \: a =  \frac{1}{2} \times  d_{1} \times  d_{2}

    using \: base \: and \: height \:  \:  \:  \:   a  = b \times h

    using \: trignometry \:  \:  \:  \:  a =  {b}^{2}  \times  \sin(a)

    where

     d_{1} = length \: of \: diagonal \: 1

    d_{2} = length \: of \: diagonal \: 2

    b= length \: of \: any \: side

    h = height \: of \: rhombus

    a = measure \: of \: any \: interior \: angle

    DERIVATION OF FORMULA:-

    The Area of the rhombus will be:

    A = 4 × area of ∆ AOB

    = 4 × (½) × AO × OB sq. units

    = 4 × (½) × (½) d1 × (½) d2 sq. units

    = 4 × (1/8) d1 × d2 square units

    = ½ × d1 × d2

    Therefore, Area of a Rhombus = A = ½ × d1 × d2

    Where d1 and d2 are the diagonals of the rhombus.

    Hope it’s clarify u

    have a great day ❣️

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