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Quadrilateral Area, Formula, Types, Properties And Examples

Quadrilateral Area, Formula, Types, Properties And Examples

We are providing you with the area of a quadrilateral, its formula, types and properties along with the solved questions. Check out the study notes here 

Quadrilateral

A quadrilateral is a 2-dimensional shape containing 4 sides. Quad means four and hence the name quadrilateral is given to the closed shapes with four sides. There are many types of quadrilaterals, each having its own properties and formula of area. We are providing you with the quadrilateral area, formula, types and its properties along with the solved questions.

Types of Quadrilateral

Quadrilaterals types can be different with varying properties. Each of the quadrilateral mentioned below has 4 sides and 4 angles. The types of quadrilaterals that we experience in our daily lives include the following:

  • Parallelogram
  • Rectangle
  • Rhombus
  • Squares
  • Trapezium
  • Kite

Quadrilateral Properties

The properties of quadrilateral include:

  • The total sum of the interior angles of a quadrilateral equals 360.
  • Every quadrilateral contains 4 sides, 4 angles and 4 vertexes.
  • Two pairs of adjacent angles of a quadrilateral sum up to 180 degrees.

Quadrilateral Area

Area of Quadrilateral: The area of quadrilateral is the region enclosed inside the sides of the figure. It has four didn’t and four angles. The area is generally defined as the region covered inside it. The quadrilateral can be regular or irregular, if a quadrilateral has all four sides equal then it is called regular or if it has all four sides having unequal length called irregular. 

The area of the quadrilateral is measured in square units and it is calculated based on the data available and the condition is given in the figure.

Quadrilateral Formula

The area of the quadrilateral is calculated as per the data available in the figure and given conditions. The area of a quadrilateral can be calculated in two ways like the traditional formula and if the given figure does not belong to such categories then the area can be found by dividing it into two parts or Hero’s formula or by using the sides of the quadrilateral.

Area of Quadrilateral = ½×length of diagonal×sum of length of the perpendicular drawn from the two vertices

Area = ½×d×(h1 + h2)

Hero’s Formula = √(s-a) (s-b) (s-c) (s-d) – and cos^2a/2

where s = a+b+c+d/2

a = a1+a2

Quadrilateral Area Calculator

The area of the quadrilateral is calculated in many ways. The quadrilateral is divided into two triangles or other methods also like Hero’s formula or sides. The formula of the area of the quadrilateral is shown above. The area of the quadrilateral can be calculated easily using the given data with the help of a formula.

Area and Parameter of Quadrilateral

As we discussed the area of the quadrilateral is the region bounded under all four sides. But the perimeter of quadrilateral is the total length of its outer boundary. A quadrilateral having four sides and four angles based on this a quadrilateral is of two types regular or irregular. A regular quadrilateral having all four sides and angles equal but an irregular quadrilateral having both unequal sides and angles. Perimeter is the total length of sides of quadrilateral. The perimeter is expressed in same as unit of length m, cm or mm.

Perimeter of quadrilateral = L1+L2+L3+L4

where L1, L2, L3, and L4 is the length of respective sides of the quadrilateral.

Parallelogram

Example. In a || gm, the adjacent sides are 36 cm and 27 cm in length. If the distance between the longer sides is 12 cm, then the distance between the smaller sides is :

एक समांतर चतुर्भुज में, आसन्न भुजाएँ की लम्बाई 36 सेमी और 27 सेमी हैं. यदि लम्बी भुजाओं के बीच की दूरी 12 सेमी है, तो छोटी भुजाओं के बीच की दूरी क्या है?

(a) 12 cm

(b) 16 cm

(c) 14 cm

(d) 15 cm

Area of Quadrilateral: Rectangle

Area of Quadrilateral: Rhombus

Example.  ABCD is rhombus in which ∠ C = 60°, then AC : BD = ? 

ABCD एक विषमकोण है जिसमें ∠ C = 60°, तो AC : BD = ?

(a) √3 : 1

(b) √3 : 2

(c) 3 : 1

(d) 3 : 2

Area of Quadrilateral: Square

Example.  ABCD is a square. M is the mid-point of AB and N is the mid-point of BC. DM and AN are joined and they meet at O. Then which of the following is correct?

ABCD एक वर्ग है. M, AB का मध्य-बिंदु है और N, BC का मध्य-बिंदु है. DM और AN जुड़े हुए हैं और वह O पर मिलते हैं. तो निम्नलिखित में से कौन सा सही है?

(a) OA : OM = 1 : 2

(b) AN = MD

(c) ∠ADM = ∠ANB

(d) ∠AMD = ∠BAN

Area of Quadrilateral: Trapezium

Example.  The parallel sides of a trapezium are in a ratio 2 : 3 and their shortest distance is 12 cm. If the area of the trapezium is 480 sq. cm., the length of the parallel sides is of length:

एक ट्रेपेज़ियम के समानांतर भुजा 2: 3 के अनुपात में हैं और उनकी सबसे कम दूरी 12 सेमी है। यदि ट्रेपेज़ियम का क्षेत्रफल 480 वर्ग सेमी है, तो समानांतर भुजा की लम्बी भुजा की लंबाई कितनी है?

(a) 56 cm

(b) 36 cm

(c) 42 cm

(d) 48 cm

Area of Quadrilateral: Examples

Q1. Find the area of quadrilateral(in unit²) AFED =? If FE∥AC & DE∥AB. If area of ∆BFE = 16 unit² and Area of ∆DEC = 9 units²

यदि FE∥AC & DE∥AB. यदि ∆BFE का शेत्रफल 16 unit² है और ∆DEC का शेत्रफल 9 units² है तो चतुर्भुज AFED का शेत्रफल ( unit² में) ज्ञात करें.

(a) 12

(b) 36

(c) 14

(d) 24

Q2. A square and a rhombus have the same base and the rhombus is inclined at 30°. What is the ratio of the area of the square to the area of the rhombus :

एक वर्ग और एक विषमकोण का समान आधार है और विषमकोण 30 डिग्री पर झुका हुआ है. वर्ग के क्षेत्रफल का विषमकोण के क्षेत्रफल से अनुपात कितना है?

(a) √2 : 1

(b) 2 : 1

(c) 1 : 1

(d) 2 : √3


Q3. The lengths of the two diagonals of a rhombus are 6 cm and 8 cm. Find the length of its perimeter (in cm).

एक विषमकोण के दो विकर्णों की लंबाई 6 सेमी और 8 सेमी है. इसकी परिधि (सेमी में) की लंबाई ज्ञात कीजिए।

(a) 20

(b) 10

(c) 40

(d) 30

Q4. In equilateral ∆ABC, find the length of altitude(in cm) put from D to BC. If, DEFG is a square & side AB = 2 + √3 cm

समबाहु ∆ABC में, यदि, DEFG एक वर्ग और भुजा AB = 2 + √3 cm है. ऊँचाई (सेमी में) ज्ञात करें यदि D से BC पर हो

(a) 3 + √3

(b) (3 + √3)/2

(c) 1.5 + √3

(d) 3 – √3

Q5. What is the measure of an interior angle of a regular polygon of 10 sides?

10 पक्षों के एक नियमित बहुभुज के आंतरिक कोण का माप क्या है?

(a) 150

(b) 156

(c) 144

(d) 160