Question

how to derive the formula of area of rhombus​

Answer 1

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 ahead ❣️

Answer 2

$\small\blue{ANSWER:-}$

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 ❣️