Table of Contents
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.
| Shape | Quadrilateral | Properties |
|---|---|---|
 |
Parallelogram |
|
 |
Rectangle |
|
 |
Rhombus |
|
 |
Square |
|
 |
Trapezium |
|
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
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
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Q6. In the given figure, PQR is a triangle and quadrilateral ABCD is inscribed in it. QD = 2 cm, QC = 5 cm, CR = 3 cm, BR = 4 cm, PB = 6 cm, PA = 5 cm and AD = 3 cm. What is the area (in cm^2 ) of the quadrilateral ABCD?
दी गयी आकृति में, PQR एक त्रिभुज है और चतुर्भुज ABCD इसमें अंकित है. QD = 2 सेमी, QC = 5 सेमी, CR = 3 सेमी, BR = 4 सेमी, PB = 6 सेमी, PA = 5 सेमी और AD = 3 सेमी. चतुर्भुज ABCD का क्षेत्रफल (cm^2 में) क्या है?
(a) (23√21)/4
(b) (15√21)/4
(c) (17√21)/5
(d) (23√21)/5
Q7. If the diagonals of a quadrilateral bisect each other and are perpendicular, the quadrilateral is:
यदि एक चतुर्भुज के विकर्ण एक दूसरे को द्विविभाजित करते हैं और लंबवत हैं, तो चतुर्भुज क्या होगा?
(a) Rhombus / विषमकोण
(b) Rectangle / आयत
(c) Parallelogram / चतुर्भुज
(d) Trapezium / समलंब
Q8. In fig ABCD is a square and PQ is the diameter of circle with center C. Find ∠PQR = ?
आकृति में, ABCD एक वर्ग है और PQ केंद्र C के वृत्त का व्यास है. ∠PQR का मान ज्ञात करें.
(a) 50°
(b) 60°
(c) 30°
(d) 20°
Q9. Find area of quadrilateral ABCD below shown as a shaded region in given figure, if out of the three squares the middle one (viz. square BHDF) has an area of 36 units². (In units²)
नीचे दिए गए आकृति में एक छायांकित क्षेत्र के रूप में नीचे दिखाए गए चतुर्भुज ABCD का क्षेत्रफल ज्ञात करें, यदि तीन वर्गों में से मध्य (अर्थात वर्ग BHDF) का क्षेत्रफल 36 इकाई² है। (इकाइयों में)
(a) 36
(b) 54
(c) 16
(d) 25
Q10. In the given figure, ABCD is a square whose side is 4 cm. P is a point on the side AD. What is the minimum value (in cm) of BP + CP?
दी गयी आकृति में, ABCD एक वर्ग है जिसकी भुजा 4 सेमी है. P, AD भुजा पर एक बिंदु है. BP + CP का न्यूनतम मान (सेमी में) क्या है?
(a) 4√5
(b) 4√4
(c) 6√3
(d) 4√6
