**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.