# The Area of any Irregular Quadrilateral

A plane figure bounded by four straight line segments is called an irregular quadrilateral. The area of any irregular quadrilateral can be calculated by dividing it into triangles.

__Example__:

Find the area of a quadrilateral $$ABCD$$ whose sides are $$9$$ m, $$40$$ m, $$28$$ m and $$15$$ m respectively and the angle between the first two sides is a right angle.

__Solution__:

From the figure we notice that $$ABD$$ is a right-angled triangle, in which $$AB = 40$$ m, $$AD = 9$$ m. Also

\[\begin{gathered} B{D^2} = A{B^2} + A{D^2} \\ B{D^2} = {40^2} + {9^2} \\ BD = \sqrt {{{40}^2} + {9^2}} = \sqrt {1681} = 41 \\ \end{gathered} \]

Now, the area of $$\Delta ABD = \frac{1}{2} \times 40 \times 9 = 180$$ m

In $$\Delta BCD$$, $$BD = a = 41$$ m, $$DC = b = 28$$ m, $$CB = c = 15$$ m

$$\therefore s = \frac{{a + b + c}}{2} = \frac{{41 + 28 + 15}}{2} = 42$$ m

Now,

\[\begin{gathered} {\text{Area}}\,{\text{of}}\,\Delta BCD = \sqrt {s(s – a)(s – b)(s – c)} \, \\ {\text{Area}}\,{\text{of}}\,\Delta BCD = \sqrt {42(42 – 41)(42 – 28)(42 – 15)} = \sqrt {42 \times 14 \times 27} = 126\,sq\,m \\ \end{gathered} \]

The area of the quadrilateral $$ABCD$$$$ = $$ area of $$\Delta ABD$$ $$ + $$area of $$\Delta BCD$$

The area of the quadrilateral $$ABCD$$ $$ = (180 + 126) = 306$$ square meters.

__Example__:

In a quadrilateral the diagonal is $$42$$ cm and the two perpendiculars on it from the other vertices are $$8$$ cm and $$9$$ cm respectively. Find the area of the quadrilateral.

__Solution__:

Given that from the figure $$AC = 42$$ m, $$BN = 9$$ m, $$DM = 8$$ m

The area of $$ABCD = $$ area of $$\Delta ABC + $$area of $$\Delta ACD$$

The area of $$ABCD$$$$ = \frac{1}{2} \times 9 \times 42 + \frac{1}{2} \times 8 \times 42 = 189 + 168 = 357$$ square meters.

D . N. SAMANTA

July 12@ 4:35 pmVery good & very easy solution

K. Gomathi

September 23@ 7:48 pmVery easy to understand. But if the angle not known and only four sides are given. How to calculate

HHA

September 14@ 6:11 pmThat’s how they calculated the area of other triangle.

praful

March 6@ 10:04 amno, what if BN ans DM is not known?

Nazim Laskar

February 12@ 10:00 amSir, will you please tell me what is the area of a quadrilater i.e. side AB=20’4″ BC=66’6″ CD=29′ DA=50′. In this angle ABC is 90 degree.

Sanjay Shyoran

September 8@ 5:57 pmSir my plot size is from South to north one west side is 198 ft and other east is 205.6 ft and from east to west from South side is 82.6ft and north side is 27.6 ft.There are 5 brothers.How to divide each share.plz solve this issue.Thanks.

Batraju Naga venkata Chaitanya

October 6@ 6:08 pmFor example if a chooses the constructing structure

It’s measurements of sides

8m width

8.5m width.

9 m length

9.3 m length

Here cross line is not available for measuring

How to calculate

Mrs.KALAISELVI

October 29@ 4:08 pmSir my plot is quadrilateral shape – total size land is 2513.58 feet . Side A=52 feet , Side B=61 feet, Side C=56 Feet and Side D=35 feet ( Side A facing road , Side B left side, Side C parallel to road and Side D right hand side). There are 2 children’s, how to divide two halves. Please give correct measures into two halves to solve this issue, by way of two method (1) horizontal and 2) straight way) and give correct feet size.

Arasan

August 25@ 11:50 pmHav u got idea to split 2 part

Mithun Mitra

October 30@ 3:47 amI have purchased a land of irregular side. What will be the area of the sides are 65 feets, 105 feets, 82 feets and 92 feets.

Swaroop Pyla

August 30@ 10:16 amCan you please give the sides lengths as based on the directions, like for example on east = x, west = y, south = a, north = b. It’ll be better if you’ve a diagonal otherwise no problem we can find it out.

RAJESH KUMAR

November 19@ 3:30 pmWE HAVE A FIELD (KHET) WHICH SHAPE LIKE IRREGULAR Quadrilateral (LONG- SIDE-1 is 90 AND SIDE-2 is 100 & (WIDTH- SIDE-1 is 10 AND SIDE-2 is 30) HOW TO DIVIDE IN 2 PART OF THIS IN BOTH SIDE (LONG-2 & WIDTH-2)

PLS SUGGEST AND GIVE FORMULA

Ramesh

January 12@ 7:49 pmSir, I need the Area in acres of an irregular quadrilateral measures given below..

North side – 450 feets

South side – 340 feets

East side – 380 feets

West side- 480 feets

Swaroop Pyla

August 30@ 10:41 amArea would be 167009.13 Sft = 15515.50 Sq.Mts = 18556.50 Sq.Yds

Nehal

January 13@ 8:56 pmHow will apply your formula on a square 400 fts each side and a rhombus of same length

R Ravi

February 6@ 3:43 pmMy plot sizes are as follows:-

Eastern side from North to South 59 feet

Western side from North to south 62.5 feet

Northern side from East to west 31 feet

Southern side from East to west 40 feet

There is 7 feet ply on the North East side

I want to know how to calculate the area of my site please

hapsa

April 9@ 5:14 pmmy plot size is 30 meters by 29 by 17 by 12 meters. how can i get the total area?

Deepak

May 9@ 12:29 pmSir my plot having four sides of 45, 27, 30, 31 meters respectively. Please help me to calculate the area and deviding this into 6 people…pls sir kindly divide.

RANVIR SINGH

June 15@ 10:13 amRespected sir/madam I want to calculate the area of my plots no. sides are 41.5833 feet, 44.5 feet, 41.8333 feet, 44.75 feet

mohammed ali

June 21@ 12:27 pmArea of ΔBCD = √42(42–41)(42–28)(42–15)=√42×14×27=126 sqm ????

CAN YOU PLEASE EXPLAIN THIS

Vipan Aggarwal

September 5@ 9:31 pmMy plot’s sides are 19.33ft, 17.0ft, 43.58 ft and 45.66 ft. What will be the area of my plot

Humberto Alarcón

October 15@ 3:56 amHow can we find the diagonal length if it’s not given and no right angles….??

North = 12.05m

West = 8.00m

South = 15.00m

East = 10.17m

Ma.socorro tagamolila

March 4@ 7:02 pmNortheast 22.31 meters,northwest 25.03 meters, southwest 24.55 meters,southeast 25.61 meters

Gary

June 10@ 8:18 pmIn your first example of quadrilateral with sides of 9,40, 28 and 15, ABD is 180 sq meters but no chance that BCD is 126…it is at least 210 sq meters…..

benard w

October 4@ 8:40 pmHello sir, I have a piece of land with theses sides: north-72metres, south-72metres, east-25metres, west-12metres. Can you help me calculate the total area of this plot?

Amol

January 8@ 7:55 pmMy plot is 171.5 by 164 feet and 34.3 by 33.3. What is the area?

Islam Eldeeb

March 20@ 2:50 pmNorth 528.54

South 9.74

East 875.56

West 708.06

Please calculate the area of this project.

Islam Eldeeb

March 20@ 2:56 pmNorth 528.54 Meter

South 9.74 Meter

East 875.56 Meter

West 708.06 Meter

what will be the area in m2

Ghazane

March 31@ 3:04 pmNeed the area of

46ft

151ft

224 ft

300 ft

Karan Singla

April 25@ 7:04 pmSouth side 55inch north side 63 inch. East side 83.33 inch and west side 57.8. Find the area..

P R Wray

August 27@ 5:27 pmIn the diagram above you have the figure 42 as the length of AB, not as the length of AC.

shashikant

January 26@ 12:28 pmEast 202 feet

west 218 feet

South 96 feet

North 102 feet

Square feet and Gunte?