derive the formula of trapezium and rhombus.​

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