Derive the formula of trapezium and rhombus.
Answers
Answer:
The area of a trapezium can be calculated using the formula: A = ½ × (a + b) × h.
Step-by-step explanation:
hope it helps!
■ Area of Trapezium Formula
The area of a trapezium can be calculated using the lengths of two of its parallel sides and the distance (height) between them. The formula to calculate the area (A) of a trapezium using base and height is given as,
A = ½ (a + b) h where,
a and b = bases of trapezium, and,
h = height (the perpendicular distance between a and b)
■ 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 AC and BD.
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, the Area of a Rhombus = A = ½ × d1 × d2
Where d1 and d2 are the diagonals of the rhombus.
Hope it is help you.