# Geometry Formulas for Class 9

## What is Geometry?

Geometry is known to be a branch of mathematics that studies the sizes, shapes, positions angles, and dimensions of things. Flat shapes like circles, squares, and triangles are a part of flat geometry and are known as 2D shapes. These shapes have only 2 dimensions, that are the length and the width.

The definition of geometry. Geometry is a branch of math that focuses on the relationship and measurement of lines, angles, solids, surfaces, and points. An example of geometry can be the calculation of a triangle's angles.

Below Mentioned are the Geometry Formulas for Class 9:

### Formulas for Solid Shapes

Here is the list of formulas for class 9 geometry:

1) Geometry Formulas for Class 9 (Square)

Area of Square:

The formula for Area of a square (A) = a2, where  A = Area of a square, a = Side of a square

The Perimeter of Square:

The formula for Perimeter of a Square (P) = 4 × a, where P = Perimeter of a square, a = Side of a square

2) Rectangle

The Perimeter of the Rectangle:

P = 2 × ( L+ B), where P = Perimeter of a rectangle, L = Length of a rectangle, B = Breadth of a rectangle.

Area of the Rectangle:

A = L × B, where A = Area of a rectangle, L = Length of a rectangle, B = Breadth of a rectangle.

3) Cuboid

Lateral Surface Area: 2h(l + b)

Total Surface Area: 2(lb + bh + hl)

Volume: l × b × h

Where l = length,b = breadth,h = height

4) Cube

Lateral Surface Area: 4(a)2

Total Surface Area: 6(a)2

Volume: (a)3

a = Sides of a cube

4) Right Circular Cylinder

Lateral Surface Area: 2(π × r × h)

Total Surface Area: 2πr (r + h)

Volume: π × (r)2 × h

Where r = radius, h = height

5) Sphere

Lateral Surface Area: 4 × π × (r)2

Total Surface Area: 4 × π × (r)2

Volume: 4/3 × (πr)3

6) Prism

Lateral Surface Area: p × h

Total Surface Area: LSA × 2B

Volume: B × h

p = perimeter of the base,

B = area of base, h = height

Above mentioned were the list of formulas for class 9 geometry.

### Formulas for Triangle

A triangle is a closed geometric figure formed by three sides and three angles.

1. Two figures are said to be congruent if they have the same size and same shape.

2. If the two triangles ABC and DEF are congruent under the correspondence that A ↔ D, B ↔ E and C ↔ F, then symbolically, these can be expressed as ∆ ABC ≅ ∆ DEF.

Right Angled Triangle: Pythagoras Theorem: Suppose ∆ ABC is a right-angled triangle with AB as the perpendicular, BC as the base and AC as the hypotenuse; then Pythagoras Theorem will be expressed as:

Hypotenuse2 = Perpendicular2 + Base2

i.e. AC2 = AB2 + BC2

### Formulas for Areas of Parallelograms and Triangles

A parallelogram is a type of quadrilateral that contains parallel opposite sides.

1. Area of a parallelogram is equal to Base × Height.

2. Area of a Triangle is equal to ½ × Base × Height.

### Class 9 Maths Formulas for Circle

A circle is a closed geometric figure. All points on the boundary of a circle are equidistant from a fixed point inside the circle (called the center).

1. Area of a circle (of radius r) = π ×(r)2

2. The diameter of the circle, d = 2 × r

3. Circumference of the circle equals 2 × π × r

4. Sector angle of the circle, θ = (180 × l ) / (π × r )

5. Area of the sector = (θ/2) × (r)2; where θ is the angle between the two radii

6. Area of the circular ring = π × ( (R)2(r)2;); where R – radius of the outer circle and r – radius of the inner circle

### Class 9 Maths Heron’s Formula

Heron’s Formula is used to calculate the area of a triangle whose all three sides are known. Let’s suppose the length of three sides is a, b and c.

Step 1 – Calculate the semi-perimeter, $s = \frac{(a+b+c)}{2}$

Step 2 – Area of the triangle = $\sqrt{s(s - a)(s - b)(s - c)}$

list of formulas for class 9 geometry:

## Coordinate Geometry Class 9 Formulas

 General Form of a Line (distance formula class 9) Ax + By + C = 0 Slope Intercept Form of a Line (distance formula class 9) y is equal to mx + c, where, m is equal to the slope Point Slope Form (distance formula class 9) y − y1= m(x − x1) where m is equal to the slope The slope of a Line Using General Equation m = −(A/B) Intercept Formula (coordinate geometry class 9 formulas) x/a + y/b = 1

Above mentioned are the coordinate geometry class 9 formulas.

### Solved Questions

Question 1) A triangle named PQR has sides where a equals to 4, b equals to 13 and c equals to 15. Find the area of the given triangle PQR using Heron’s Formula.

Answer) Semiperimeter of triangle PQR, s = (4+13+15)/2 = 32/2 = 16

By heron’s formula, we know;

Area is equal to $\sqrt{s(s - a)(s - b)(s - c)}$

Hence, Area is equal to $\sqrt{16(16 - 4)(16 - 13)(16 -15)} = \sqrt{(16 \times 12 \times 3 \times 1)} = \sqrt{576} = 24$

The heron’s formula is applicable to all types of triangles.

Question 1) What are the Coordinate Geometry Formulas for Class 9?

Answer) The coordinate geometry formulas for class 9 for finding the area of any given rectangle is A = length × width. When finding the area of a triangle, the formula area = ½ base × height. As an example, to find the area of a triangle with a base b measuring 2 cm and a height h of 9 cm, multiply ½ by 2 and 9 to get an area of 9 cm squared.

Therefore it is the coordinate geometry formulas for class 9.

Question 2)How do you Find the Area?

Answer) The simplest (and most commonly used) area calculations are for squares and rectangles. Now to find the area of a rectangle, multiply its height by its width. In the case of a square, you only need to find the length of one of the sides (as each side is the same length) and then it can be multiplied by itself to find the area.

Question 3) What are the 3 Types of Geometry?

Answer) In two dimensions there are 3 geometries: Euclidean, spherical, and hyperbolic. These are the only geometries possible for 2-dimensional objects, although a proof of this is beyond the scope of this book.

Question 4) What is the Formula of Volume?

Answer) The formula that is required to find the volume multiplies the length by the width by the height. The good news in the case of a cube is that the measure of each of these dimensions is exactly the same. Therefore, you can easily multiply the length of any side three times and that will help us find the volume. This results in the formula: Volume is equal to side × side × side.