# RS Aggarwal Class 8 Chapter 18 Solutions (Area Of A Trapezium And A Polygon)

RS Aggarwal Class 8 Maths Solutions for Chapter 18 ‘Area of a Trapezium and A Polygon’ provide clear explanations of the topics of the chapter. In this chapter of RS Aggarwal Class 8 Maths Solutions, you will study what are trapeziums, their properties, and how to find their area. You will also study how we can find the area of different polygons such as a hexagon, pentagon, or octagon. The important points related to the chapter topics are given below on this page for a quick overview.

This chapter is a continuation of previous geometry chapters of quadrilaterals and polygons and contains advanced topics related to quadrilaterals and polygons. There are 3 exercises in this chapter with 25 practice questions in total. All these questions are designed to ensure that you grasp the concepts of the chapter thoroughly and can use the formulas described in the chapter in your exams.

The concepts explained in Chapter 18 ‘Area of a Trapezium and A Polygon’ are easy to understand but there can be chances that you get confused with the different properties of quadrilaterals. Instasolv provides complete solutions to all three exercises of this chapter for your assistance. These solutions will solve your doubts instantly and will help you prepare this chapter for your exams.

## Important Topics for RS Aggarwal Class 8 Maths Solutions Chapter 18: Area of a Trapezium and A Polygon

**Trapezium**

- A trapezium is a quadrilateral. It has four sides where any two sides are parallel to each other. It is also referred to as Trapezoid.
- This is why a trapezium is also called a parallelogram. We can also call it a polygon as it has many sides.
- Just like all other quadrilaterals, the sum of interior angles of a trapezium is 360°.
- The pair of adjacent angles in a trapezium for a sum of 180°.
- The parallel sides of the trapezium are called ‘bases’ and the non-parallel sides are called ‘legs’.
- The trapezium has two diagonals and these diagonals bisect each other. This means that the diagonal divide each other into two equal parts at the point of intersection.
- If we draw a line joining the mid-points of the legs of the trapezium, that line is parallel to the bases of the trapezium.

**Types of Trapeziums**

**Isosceles trapezium**– It is a trapezium in which the legs have the same length.**Scalene Trapezium**– It is a trapezium in which all the angles and sides (the bases and the legs) are of different measures.**Right Trapezium**– It is a trapezium in which there are at least two right angles.

**Important Formulae related to Trapeziums **

**Area of Trapezium**= ½ height (sum of its legs)**Perimeter of Trapezium**= sum of all its sides**Length of Mid-Segment**= ½(Sum of the length of the bases)

**Area of Regular Polygons **

You must know that a polygon is any two-dimensional, closed shape with three or more sides. The polygons which have equal sides and equal interior angles are called regular polygons while the polygons which do not have equal sides or equal interior angles are called irregular polygons.

Type of Polygon |
Area of Polygon |

Triangle | ½ x Base x Height |

Rectangle | Length x Breadth |

Square | Length^{2} |

Parallelogram | Base x Height |

Trapezium | ½ Height (Sum of its Legs) |

Rhombus | ½ x Diagonal_{1} x Diagonal_{2} |

**Area of Irregular Polygons **

In the case of irregular polygons, we divide the polygons in such a way that it becomes a combination of regular polygons. Hence we find the area of each regular polygon in order to find the area of an irregular polygon. Consider the image given below:

This is an irregular pentagon ABCDE. However, you can observe that this pentagon comprises of three triangles: AEN, DMC, and ABC. Also, there is a trapezium EDMN. So the area of pentagon can be calculated by adding the areas of AEN, DMC, ABC, and Trapezium EDMN.

### Exercise Discussion for RS Aggarwal Class 8 Maths Solutions Chapter 18: Area of a Trapezium and A Polygon

- RS Aggarwal Class 8 Maths Solutions for Chapter 18 ‘Area of a Trapezium and A Polygon’ comprise three exercises. Exercise 18A has 12 questions, Exercise 18B has 8 questions and Exercise 18C has 5 questions respectively.
- In exercise 18A, the questions are related to finding the area of trapezium. Some questions are straightforward where you are given the length of the bases and the height of the trapezium and you can apply the formula and get the answer.
- But, there are also questions where you are given the area of the trapezium and you have to find the two parallel sides.
- Exercise 18B has questions related to finding the area of irregular polygons like an irregular pentagon and irregular hexagon.
- Exercise 18C also has questions about finding the area of trapezium. These questions are slightly difficult and involve more calculations.

### Benefits of RS Aggarwal Class 8 Maths Solutions Chapter Chapter 18: Area of a Trapezium and A Polygon

- RS Aggarwal Solutions for Class 8 Maths Chapter 18 are prepared in a simple and step by step format by our subject matter experts.
- We have included clear diagrams and explanations for every question of finding the area of a trapezium or a polygon.
- You will find the RS Aggarwal Class 8 Maths Chapter solutions by the maths expert team compatible with your CBSE Class 8 Maths syllabus.
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