hey! the question is to figure out the formula of rhombus....
Answers
Derivation of area of rhombus:
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.
Formulas to calculate the area of Rhombus:-
- using diagonals: A=½×d1×d2
- using base and height: A=b×h
- using trigonometry: A=b²×sin(a)
Where,
Where,d1 = length of diagonal 1
Where,d1 = length of diagonal 1d2 = length of diagonal 2
Where,d1 = length of diagonal 1d2 = length of diagonal 2b = length of any side
Where,d1 = length of diagonal 1d2 = length of diagonal 2b = length of any sideh = height of rhombus
Where,d1 = length of diagonal 1d2 = length of diagonal 2b = length of any sideh = height of rhombusa = measure of any interior angle
derivation of rhombus area 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.
