derive the formula of trapezium and rhombus.
Answers
Answer:
Area of trapezium = ½ x (a+b) x h
Perimeter of trapezium = a+b+c+d
Where a, b, c and d are the length of sides of a trapezium
And h is the distance between the two parallel sides i.e., a and b.
FAQ's on Rhombus Formulas
The formulae for rhombuses are defined for two parameters, area and perimeter: Area of a rhombus = 1/2 × d1 d 1 × d2 d 2 , where d1 d 1 and d2 d 2 are diagonals of a rhombus. The perimeter of a rhombus, where P = 4 × a, where 'a' is the side of the rhombus.
Step-by-step explanation:
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Answer:
Area of a Trapezium Formula
Trapezium area can be calculated by using the below formula:
Area = (1/2) h (a+b)
where,
a and b are the length of parallel sides/bases of the trapezium
h is the height or distance between parallel sides.
Area Of Trapezium
From the figure, area of trapezium = 1/2 (AB + DC).h
Perimeter of Trapezium
The perimeter of trapezium formula is given by:
Perimeter = Sum of all the sides = AB + BC + CD + DA
Derivation of Area of a Trapezium
Following is the derivation for computing the area of the trapezium:
The area of a trapezoid is equal to the sum of the areas of the two triangles and the area of the rectangle.
We know that
area of trapezoid = area of triangle 1 + area of rectangle + area of triangle 2.
That means,
A = (ah/2) + b1h + (ch/2)
A = (ah + 2b1h + ch)/2
Simplifying the equation, rearranging the terms, and factoring result to:
A = h/2[b1 + (a + b1 + c)] ….(i)
If we assume the longer base of the trapezoid be b2, then
b2 = a + b1 + c …..(ii)
Substituting (ii) in equation (i),
A = h/2(b1 + b2)
Therefore, the area of a trapezoid with bases b1, b2 and altitude h is;
A = h/2(b1+b2)
How to Calculate Area of Trapezium?
To find the area of a trapezium, follow the below-given steps:
Step 1: Find the dimensions of given trapezium, i.e., length of parallel sides and length of height.
Step 2: Add the length of parallel sides
Step 3: Multiply the sum of parallel sides with the height of trapezium
Step 4: Now, multiply the above-calculated value by 1/2 to get the final answer
The obtained value in step 4 is the area of the given trapezium.
Video Lesson on Area of Trapezium