2D Shapes Formulas
Introduction
In mathematics, 2D shapes are geometric figures that can be drawn on a flat surface. These shapes have various properties and formulas to calculate their perimeter, area, and other characteristics. In this article, we will discuss the formulas for different 2D shapes.
Square
A square is a quadrilateral with four equal sides and four right angles.
Formulas:
- Perimeter: 4 × side (P = 4s)
- Area: side × side (A = s^2)
Rectangle
A rectangle is a quadrilateral with four sides and four right angles, where opposite sides are equal.
Formulas:
- Perimeter: 2 × (length + width) (P = 2(l + w))
- Area: length × width (A = lw)
Triangle
A triangle is a polygon with three sides and three vertices.
Formulas:
- Perimeter: side1 + side2 + side3 (P = a + b + c)
- Area: (base × height) / 2 (A = (b × h) / 2)
Circle
A circle is a set of points equidistant from a central point called the center.
Formulas:
- Circumference: 2 × π × radius (C = 2πr)
- Area: π × radius × radius (A = πr^2)
Rhombus
A rhombus is a quadrilateral with four equal sides and opposite sides are parallel.
Formulas:
- Perimeter: 4 × side (P = 4s)
- Area: (diagonal1 × diagonal2) / 2 (A = (d1 × d2) / 2)
Trapezoid
A trapezoid is a quadrilateral with two pairs of opposite sides, where one pair is parallel.
Formulas:
- Perimeter: side1 + side2 + side3 + side4 (P = a + b + c + d)
- Area: (height × (base1 + base2)) / 2 (A = (h × (b1 + b2)) / 2)
Parallelogram
A parallelogram is a quadrilateral with two pairs of opposite sides that are parallel.
Formulas:
- Perimeter: 2 × (side1 + side2) (P = 2(a + b))
- Area: base × height (A = bh)
Hexagon
A hexagon is a polygon with six sides and six vertices.
Formulas:
- Perimeter: 6 × side (P = 6s)
- Area: ((3 × sqrt(3)) / 2) × side × side (A = ((3 × √3) / 2) × s^2)
Octagon
An octagon is a polygon with eight sides and eight vertices.
Formulas:
- Perimeter: 8 × side (P = 8s)
- Area: (2 + 4 / cot(π / 8)) × side × side (A = (2 + 4 / cot(π / 8)) × s^2)
These are the common formulas for 2D shapes. Understanding and applying these formulas will help you solve various problems in mathematics and real-life applications.
