what is the formula of rhombus
Answers
Answer:
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Step-by-step explanation:
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What is the Area of a Rhombus?
The area of a rhombus can be defined as the amount of space enclosed by a rhombus in a two-dimensional space. To recall, a rhombus is a type of quadrilateral projected on a two dimensional (2D) plane, having four sides that are equal in length and are congruent. It is also known as equilateral quadrilateral because all its four sides are equal in nature.
Area of Rhombus Formula
Different formulas to find the area of a rhombus are:
Formulas to Calculate Area of Rhombus
Using Diagonals A = ½ × d1 × d2
Using Base and Height A = b × h
Using Trigonometry A = b2 × Sin(a)
Where,
d1 = length of diagonal 1
d2 = length of diagonal 2
b = length of any side
h = height of rhombus
a = measure of any interior angle
Derivation for Rhombus Area Formula
Consider the following rhombus:
Area of a Rhombus Derivation
Let O be the point of intersection of two diagonals.
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.