NCERT Solutions for Class 8 Maths Chapter 9 Exercise 9.1 Mensuration in Hindi and English Medium updated for CBSE session 2024-25. All the question-answers and explanation of ex. 9.1 class 8th mathematics are revised according to revised syllabus and latest NCERT textbooks issued for academic year 2024-25.

## 8th Maths Exercise 9.1 Solution in Hindi and English Medium

Class: 8 | Mathematics |

Chapter: 9 | Exercise: 9.1 |

Topic Name: | Mensuration |

Content: | NCERT Exercise Solutions |

Content Mode: | Text and Videos |

Academic Year: | CBSE 2024-25 |

Medium: | Hindi and English Medium |

### Class 8 Maths Chapter 9 Exercise 9.1 Solution

Class VIII Mathematics Ex. 9.1 Mensuration in Hindi Medium and English Medium free download in PDF for session 2024-25 CBSE exams. Here we will learn to find the area of quadrilaterals in various ways. NCERT Book Exercise 9.1 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.

#### 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**

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 9.1?

There are total 9 questions in exercise 9.1 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 9.1 of Class VIII Maths difficult?

No, the exercise is not difficult. Class VIII Maths exercise 9.1 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 9.1 of 8th Maths?

Questions 8, 9, 10, and 11 are considered as important one but the most important questions of exercise 9.1 of class 8 Maths is 10. It is asked in exams many time.