# Area of a polygon

## 1. AREA OF PARALLELOGRAM

### 1.1. SQUARE OF SQUARE

where a is the side and d is the diagonal of the square.

P = a ∙ b

### 1.3. ROMBOID AREA

The area of a rhomboid is calculated according to the following formulas:

P = a ∙ hₐ P = a ∙ b ∙ sinα

### 1.4. ROMB AREA

The formulas for calculating the area of a rhombus are:

## 2. AREA OF A TRIANGLE

The area of the triangle is equal to the half product of the side and the corresponding height, ie.

When two sides are known and the angle occupied between them, then the area of the triangle is calculated by the formulas:

The sides a, b, c, the radius of the inscribed circle r, the radius of the inscribed circle R and the area R of the triangle are related by the following formulas:

Heron formula:

## 3. AREA OF TRAPEZE AND TRAPEZOID

The area of a trapezoid is equal to the product of the sum of its sides and the height, ie.

The area of a quadrilateral (trapezoid) can be calculated using Heron's formula if all sides and one of the diagonals are known (Fig. 8) and thus

If the quadrilateral has normal diagonals (e.g. deltoid, fig.9), then its area can be calculated by the formula:

## 4. PERIMETER AND AREA OF A REGULAR POLYGON

The equilateral triangle AOV is called the characteristic triangle of the regular n-angle

The sides a, the radii R and r of the described and inscribed circle of the regular n-angle are elements of the characteristic triangle. The following formulas are correct for the characteristic AOV triangle:

The perimeter of a regular n-angle is calculated by the formula:

The area of a regular nangle is calculated by the formula:

• Video Lesson – Polygon Area:

• Video lesson – Area of a triangle:

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