RS Aggarwal Solutions Class 9 Maths Chapter 14 Areas of Triangles and Quadrilaterals (Updated For 2024)

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RS Aggarwal Solutions Class 9 Maths Chapter 14 Areas of Triangles and Quadrilaterals

RS Aggarwal Solutions Class 9 Maths for Chapter 14 Areas of Triangles and Quadrilaterals – Overview

In Chapter 14 of RS Aggarwal Solutions Class 9 Maths, you will get to know about the following topics:

1. Area of different triangles and quadrilaterals
2. Area of quadrilaterals using diagonals

In this chapter, you will have to deal with two exercises:

1. There are 44 questions in the first exercise that covers various concepts of finding the area of triangles and different quadrilateral figures using suitable formulae.
2. In the second exercise, there are various objective-type questions based on the concepts you have learned in the previous exercise.

• Important Formulae

1. The basic area of any triangle: ½  × b × h

where b is the base and h is the height of the triangle

2. Area of an equilateral triangle: An equilateral triangle is a triangle whose all sides are equal.

Area of an equilateral triangle = √3/4 × a²

Height of an equilateral triangle = √3/4 × a

where a is the measure of its sides.

3. Area of an isosceles triangle: b/4 x √4a²-b²

where a is the measure of the two equal sides and b is the measure of the base.

4. Area of a triangle having three different sides (Heron’s formula):- 

Suppose a triangle has sides measuring a, b, and c. 

According to Heron’s formula:-

The first step includes finding the semi-perimeter of the triangle:

Semi-perimeter (S) = (a+b+c)

Using the above finding and implementing it in Heron’s formula for the area of a triangle constitutes the second step.

Area = √ s (s-a) (s-b) (s-c)

There are seven different types of quadrilaterals, each having a specific formula for its area.

1. Parallelogram: Its opposite sides are equal and parallel to each other.

Area of a parallelogram = base × height

2. Rectangle: It is a parallelogram with all four angles measuring 90⁰

Area of a rectangle = length × breadth

3. Square: It is a rectangle whose all sides are equal

Area of a square = side²

4. Rhombus: It is a parallelogram whose all sides are equal.

Area of a rhombus = base × height

Area of rhombus using diagonals = (d1xd2)/2

5. Trapezium: A trapezium has one pair of sides parallel. 

Area of trapezium = 1/2 x (a + b) × h

where a and b are the measure of two parallel-sided and h is the height

6. Kite: It has two pairs of equal adjacent sides but unequal opposite sides.

Area of a kite = (d1xd2)/2

NOTE: The perimeter of any figure is equal to the sum of all its sides.

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