NCERT Solutions for Class 8 Maths Chapter 11 Exercise 11.2 in Hindi and English Medium updated for CBSE session 2022-2023.

Class 8 Maths Chapter 11 Exercise 11.2 Solution

Class VIII Mathematics Ex. 11.2 Mensuration in Hindi Medium and English Medium free download in PDF for session 2022-23 CBSE exams. Here we will learn to find the area of quadrilaterals in various ways. NCERT Book Exercise 11.2 of grade 8 mathematics deals the questions based on application of areas of quadrilateral. Sometime it can be calculated using triangles otherwise it depends on the situation.

Class: 8Mathematics
Chapter: 11Exercise: 11.2
Topic Name:Mensuration
Content:NCERT Exercise Solution
Content Mode:Text and Videos
Medium:Hindi and English Medium

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Area of a Polygon

We know that the plots and fields are generally in the form of regular or irregular polygons. We find their areas by dividing them into triangles, rectangles, parallelograms and trapeziums.

Area of a Quadrilateral

Let ABCD be a given quadrilateral in which BD is one of its diagonals.
Let AL Ʇ BD and CM Ʇ BD.
Let AL = h and CM = h. Then,
area of quad. ABCD
= ar(DABD) + ar(DBCD)
= ½ x BD x AL + ½ x BD x CM
= ½ x BD x h + ½ x BD x h
= ½ x BD x (h + h) sq. units.

ABCD is a quadrilateral in which BD = 14 cm, AL Ʇ BD, CM Ʇ BD such that AL = 6 cm and CM = 8 cm. Find the area of quad. ABCD.
Area of quad. ABCD = ar (triangle ABD) + ar (triangle BCD)
= {½ x BD x AL + ½ x BD x CM} cm²
= {½ x 14 x 6 + ½ x 14 x 8} cm²
= (42 + 56) cm2 = 98 cm²
Area of Irregular Polygon

Find the area of the given pentagon ABCDE in which each one of BF, CH and EG is perpendicular to AD such that AF = 9 cm, AG = 13 cm, AH = 19 cm, AD = 24 cm, BF = 6 cm, CH = 8 cm and EG = 9 cm.
Area of the given pentagon ABCDE
= {1/2 x AF x BF + ½ x (BF + CH) x FH} + {½ x HD x CH + ½ x AD x EG}
= {1/2 x AF x BF} + {½ x (BF + CH) x (AH – AF)} + {1/2 x (AD – AH) x CH} + {1/2 x AD x EG}
= {1/2 x 9 x 6} + {½ x (6 + 8) x (19 – 9)} + {1/2 x (24 – 19) x 8} + {1/2 x 24 x 9} cm²
= (27 + 70 + 20 + 108) cm² = 225 cm².
Area of Regular Polygons
Q Find the area of the given regular hexagon ABCDF in which each side measures 5 cm, height BE = 11 cm and width FD = 8 cm.
Join BE. Then, = ar(hexagon. ABCDF) = 2 x ar(trap. ABEF) + ar(trap. BCDE)
= 2 x ½ x (AF + BE) x FL, where FL Ʇ BE
= 2 x ½ x (5 + 11) x 4 cm² (Because FL = 1/2FD = 4 cm)
= 64 cm²

What are the properties of trapezium?
Properties of a Trapezium:
A trapezium has two parallel sides and two non-parallel sides.
The diagonals of regular trapezium bisect each other.
The length of the mid-segment is equal to half the sum of the parallel bases, in a trapezium.

Are diagonals equal in a trapezium?
Diagonals are equal only in the special case of trapezium that is known as a trapezoid (or isosceles trapezium). Furthermore, a characteristic property of trapezoid is that the diagonals happen to be equal.

Can a trapezium have a right angle?
A trapezium cannot have four right angles. A trapezium is a quadrilateral, which means that it has four sides and four angles.

What angles does a trapezium have?
A trapezium has four angles. Regardless of whether you use the British or U.S. definition, a trapezium is a quadrilateral. This means that it is a polygon with four sides. Since all polygons have the same number of sides as they have angles, a trapezoid has four sides and four angles.

How many questions are there in class 8 Maths exercise 11.2?

There are total 11 questions in exercise 11.2 of 8th mathematics. All the questions are based on the concept dividing the quadrilateral in two triangle to find area. Questions are based on formulae and calculation.

Is exercise 11.2 of Class VIII Maths difficult?

No, the exercise is not difficult. Class VIII Maths exercise 11.2 is lengthy in calculation but easy in concepts. Questions 1 to 7 of exercise are easy to solve but question 8 to 11 are tricky.

Which is the most important questions of exercise 11.2 of 8th Maths?

Questions 8, 9, 10, and 11 are considered as important one but the most important questions of exercise 11.2 of class 8 Maths is 10. It is asked in exams many time.

NCERT Solutions for Class 8 Maths Chapter 11 Exercise 11.2
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