Geometry is a branch of mathematics that deals with the shapes and sizes of figures. It is a very important subject for students in class 8, as it helps them understand the world around them better. Geometry formulas are a set of equations that help us calculate the dimensions of various geometric figures. There are many different geometry formulas for class 8, but some of the most important ones are listed below.
What Is Geometry?
There are a few things that you should know about geometry before we get started on the formulas. Geometry is the branch of mathematics that studies the size, shape, and position of figures in space. A figure is any two-dimensional or three-dimensional object, such as a circle, square, triangle, or cube.
In order to describe the size, shape, and position of figures, we use a variety of terms and notation. We will go over some of the most important terms and notation in this section.
Size: When we talk about the size of a figure, we are usually referring to its area or volume. The area of a two-dimensional figure is the amount of space it occupies on a flat surface. The volume of a three-dimensional figure is the amount of space it occupies in space.
Shape: The shape of a figure is determined by its edges and vertices (plural for vertex). An edge is a line segment that connects two vertices. A vertex is a point where two or more edges meet.
Position: The position of a figure can be described by its orientation and location. Orientation refers to the way the figure is oriented in space. Location refers to the specific place where the figure is located.
The Different Types of Geometry
Geometry is a branch of mathematics that studies the properties and relations of points, lines, surfaces, solids, and higher-dimensional analogues. There are different types of geometry, including: -Euclidean geometry: This is the kind of geometry that most people learn in school. It is based on a small set of axioms (self-evident truths) that are used to deduce other truths. -Non-Euclidean geometry: This is a type of geometry that deviates from Euclidean geometry. It includes hyperbolic geometry and elliptic geometry. -Riemannian geometry: This is a type of geometry that takes into account the curvature of surfaces.
Euclidean geometry is the study of shapes and figures that exist in two dimensions. This type of geometry is named after the Greek mathematician Euclid, who first developed its principles. Euclidean geometry is distinguished from other types of geometry by its use of axioms, or self-evident truths. These axioms include the existence of points, lines, and planes; the ability to draw a line between any two points; and the existence of parallel lines. Other properties of Euclidean geometry include the sum of the angles in a triangle, and the Pythagorean theorem.
Non-Euclidean geometry is a branch of mathematics that studies spaces with curvature, such as the surface of a sphere. In the late 19th century, it was found that the geometry of our universe is non-Euclidean.
One of the most famous examples of non-Euclidean geometry is the Poincaré disk model of hyperbolic geometry. In this model, the space inside a circle is considered to be infinitely large, and the straight lines are replaced by arcs of circles. This gives rise to some counterintuitive results, such as the fact that there are an infinite number of parallel lines through any given point.
Non-Euclidean geometry has applications in many fields, including physics and cosmology. It is also useful for studying certain problems in computer science, such as network routing.
In projective geometry, points are considered to be equivalent if they lie on the same line. This means that parallel lines never meet, and that any two lines can be extended to meet at a point. Projective geometry is a useful tool for studying perspective drawings, since all such drawings are equivalent to projective geometry.
In Euclidean geometry, points are considered to be equivalent if they have the same coordinates. However, in affine geometry, points are considered to be equivalent if they are related by an affine transformation. This means that, in affine geometry, points can be moved, rotated, or scaled without changing their properties.
Affine transformations include translation, rotation, reflection, and dilation. All of these transformations preserve the straightness of lines and the parallelism of lines. This is in contrast to non-affine transformations, such as perspective distortions.
Affine geometry is a branch of mathematics that studies figures that are invariant under affine transformations. This includes many shapes that are not included in Euclidean geometry, such as parabolas and hyperbolas. Affine geometry has been studied since the time of Euclid, and its principles are used in many fields, including computer graphics and engineering.
The Basic Geometry Formulas for Class 8
There are a few basic geometry formulas that you should memorize for class 8. These include:
– The area of a rectangle is A = lw (where l is the length and w is the width)
– The area of a triangle is A = 1/2bh (where b is the base and h is the height)
– The circumference of a circle is C = 2πr (where r is the radius)
– The volume of a cylinder is V = πr2h (where r is the radius and h is the height)
List of Geometry Formulas For Class 8
The below table knowledge glow provides you a few important geometry formulas for class 8. The all formulas listed below are commonly required in class 8 geometry to calculate volumes, lengths and areas.
Geometry Shapes Formulas for Class 8
|Name of the Solid||Lateral / Curved Surface Area||Total Surface Area||Volume|
|Right Pyramid||½ × Perimeter of Base × Slant Height||Lateral Surface Area + Area of the Base||⅓ × (Area of the Base) × height|
|Right Prism||Perimeter of base × height||Lateral Surface Area + 2(Area of One End)||Area of Base × Height|
|Right Circular Cylinder||2πrh||2πr(r+h)||πr2h|
|Right Circular Cone||πrl||πr(l+r)||⅓ × πr2h|
|Sphere||4πr2||4πr2||4/3 × πr3|
|Hemisphere||2πr2||3πr2||2/3 × πr3|
How to Use the Formulas
Assuming you are referring to a Euclidean plane, the following is a list of basic geometric formulas that are frequently used in solving problems. It is recommended that you memorize these formulas as they will be very useful in solving plane geometry problems.
- Area of a square: A = a2
- Area of a rectangle: A = lw
- Area of a parallelogram: A = bh
- Area of a triangle: A = 1/2bh
- Area of a trapezoid: A = 1/2(b1 + b2)h
- Circumference of a circle: C = 2πr or C = πd where d is the diameter.
- Arc length formula: L=rθ where θ is in radians.
- Area of sector formula: A=r2θ where θ is in radians.
Geometry is a fascinating subject, and these formulas are just a taste of what you can learn in this math discipline. If you’re enrolled in a geometry class, studying for tests and exams will be much easier if you have all the formulas at your fingertips. And, even if you’re not currently taking a geometry class, it can’t hurt to brush up on these formulas – who knows when they might come in handy!
Important Question and answers on Geometry
What is the most basic shape in geometry?
The most basic shape in geometry is the point. A point has no dimensions and is represented by a dot. Points are used to define lines and planes.
What is a line?
A line is a straight path between two points. A line has no width, thickness, or other size; it is infinitely thin. Lines are used to define angles and polygons.
What is an angle?
An angle is formed when two lines intersect at a point. The angle is the amount of turn between the two lines, measured in degrees or radians. Angles are used to define polygons and circles.
What is a polygon?
A polygon is a closed figure made up of segments called sides that intersect at points called vertices. The sides of a polygon can be straight or curved. Polygons are used to define areas in plane geometry.
What is a circle?
A circle is a curve that lies equally distant from a point called the center point. The distance from the center point to any point on the circle is called the radius of the circle; the distance around the circle (the length of its circumference)is also equal to its diameter times pi.