Math, asked by jababbaba, 8 months ago

how to derive the formula of area of rhombus​

Answers

Answered by Anonymous
3

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 ❣️❗:-

Answered by Anonymous
3

EXPLANATION:-

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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