2D and 3D Shapes and Their Formulas
Introduction
Geometry is an essential branch of mathematics that deals with the study of shapes, sizes, and positions of objects. In this article, we will explore the different types of 2D and 3D shapes, their properties, and formulas.
2D Shapes
Rectangle
A rectangle is a quadrilateral with four right angles and opposite sides of equal length.
Formulas:
- Area:
A = length × width - Perimeter:
P = 2 × (length + width)
Square
A square is a quadrilateral with four equal sides and four right angles.
Formulas:
- Area:
A = side² - Perimeter:
P = 4 × side
Triangle
A triangle is a polygon with three sides and three vertices.
Formulas:
- Area:
A = (base × height) / 2 - Perimeter:
P = a + b + c(where a, b, and c are the sides of the triangle)
Circle
A circle is a set of points equidistant from a central point called the center.
Formulas:
- Area:
A = π × radius² - Circumference:
C = 2 × π × radius
Rhombus
A rhombus is a quadrilateral with all sides of equal length.
Formulas:
- Area:
A = (diagonal1 × diagonal2) / 2 - Perimeter:
P = 4 × side
Parallelogram
A parallelogram is a quadrilateral with opposite sides of equal length.
Formulas:
- Area:
A = base × height - Perimeter:
P = 2 × (base + side)
3D Shapes
Cube
A cube is a solid shape with six square faces of equal size.
Formulas:
- Volume:
V = side³ - Surface Area:
SA = 6 × side²
Sphere
A sphere is a set of points equidistant from a central point called the center.
Formulas:
- Volume:
V = (4/3) × π × radius³ - Surface Area:
SA = 4 × π × radius²
Cuboid
A cuboid is a solid shape with six rectangular faces.
Formulas:
- Volume:
V = length × width × height - Surface Area:
SA = 2 × (length × width + width × height + height × length)
Cone
A cone is a solid shape with a circular base and a curved surface.
Formulas:
- Volume:
V = (1/3) × π × radius² × height - Surface Area:
SA = π × radius × (radius + slant height)
Cylinder
A cylinder is a solid shape with two parallel and circular bases and a curved surface.
Formulas:
- Volume:
V = π × radius² × height - Surface Area:
SA = 2 × π × radius × (radius + height)
Conclusion
In conclusion, this article has covered the different types of 2D and 3D shapes, their properties, and formulas. Understanding these formulas is essential in various fields such as architecture, engineering, and design.
