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Area Of A Trapezium: Formula To Find Area Of A Trapezium Without Height

Area Of Trapezium

A Trapezium is a quadrilateral with one pair of sides parallel. Do you know how to find out the Area of Trapezium? Finding out area of Trapezium is not that much difficult but sometimes the problem rise when we are asked to Find Area of a Trapezium without Height.

Do not panic with the questions, the answers are also given her along. Yes the Formula for Area of Trapezium is available here.  Here on this page of we have structured the whole concept of Trapezium along with its formula in detail, have a look…

Area Of  Trapezium

Area Of A Trapezium:

To answer the question –
What Is The Area Of Trapezium,

Take a look over the trapezium given below:

Area Of Trapezium

Now Area Of Trapezium Formula is:

Area of trapezium ABCD = Area of ∆ ABD + Area of ∆ CBD

= 1/2 × a × h + 1/2 × b × h

= 1/2 × h × (a + b)

= 1/2 (sum of parallel sides) × (perpendicular distance between them)

For Example:

ABCD is a trapezium in which AB CD, AD DC, AB = 20 cm, BC = 13 cm and DC = 25 cm. Find the area of the trapezium. 

Area Of Trapezium Example


From B draw BP perpendicular DC

Therefore, AB = DP = 20 cm

So, PC = DC – DP

= (25 – 20) cm

= 5 cm

Now, area of trapezium ABCD = Area of rectangle ABPD + Area of △ BPC

△BPC is right angled at ∠BPC

Therefore, using Pythagoras theorem,

    BC² = BP² + PC²

    13² = BP² + 5²

⇒ 169 = BP² + 25

⇒ 169 – 25 = BP²

⇒ 144 = BP²

⇒ BP = 12

Now, area of trapezium ABCD = Area of rectangle ABPD + Area of ∆BPC

= AB × BP + 1/2 × PC × BP

= 20 × 12 + 1/2 × 5 × 12

= 240 + 30

= 270 cm²

Also Get Here: Volume And Surface Area Questions And Answers

Area Of Isosceles Trapezium

There are two isosceles trapezoid formulas:

The perimeter of isosceles trapezoid formula

The perimeter of isosceles trapezoid formula is a+b+2c

Where a, b and c are the sides of the trapezoid

Area of isosceles trapezoid formula is

Area of isosceles trapezoid= h (a+b / 2)

Where a and b are the parallel sides of trapezoid.


Question 1: A trapezoid has legs 5 cm each in length. Its bases are 10 cm and 12 cm respectively. Calculate its perimeter.


Given: a = 10 cm, b = 12 cm, c = 5 cm
Perimeter is given by
p = a + b + 2c
= 10 + 12 + 2 ×× 5
= 32 cm.

Formula to Calculate Area, Perimeter, Circumference: Find Area of Circle

Area Of Trapezium Without Height

If a question raises that How to Find Area of Trapezium without Height, then all you need to do is to apply this formula:

Area of a trapezium without knowing the height:

(a+c) / 4(a-c) * √(a+b-c+d)(a-b-c+d)(a+b-c-d)(-a+b+c+d)

Where a>c and ‘a’ is parallel to ‘c’. ‘b’ and ‘d’ are the ‘diagonals’.

Area Of Trapezium When All Sides Are Given

If in case all the sides of trapezium are given then all you need to do is to apply the regular formula to find the Area of trapezium.

Get Maths Vedic/Basic Formulas Free List: Maths Formulas

We hope the above given information will be helpful for you all in understanding the concepts of Trapezium and its formula. If you have any query regarding the same then you my mention your comments in below given comment box.

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