Area of a polygon

1. AREA OF PARALLELOGRAM

1.1. SQUARE OF SQUARE

211-f1

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

211-c1
SQUARE – Draw.1

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1.2. RECTANGULAR AREA

212-c2
RECTANGULAR – Fig.2

P = a ∙ b

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1.3. ROMBOID AREA

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

P = a ∙ hₐ P = a ∙ b ∙ sinα

213-c3
ROMBOID – Fig.3

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1.4. ROMB AREA

The formulas for calculating the area of a rhombus are:

213-f1
214-c4
ROMB
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2. AREA OF A TRIANGLE

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

214-f1
215-c5
TRIANGLE

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

215-f1
216-c6

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:

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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.

217-f1
217-c7
TABLE – Fig.7

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

218-c8
TRAPEZOID – Fig.8

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

219-c9
Deltoid – Fig.9


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4. PERIMETER AND AREA OF A REGULAR POLYGON

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

220-c10
REGULAR POLYGON – Draw. 10


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:

221-f1

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

222-f1

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

222-f2
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  • Video Lesson – Polygon Area:

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  • Video lesson – Area of a triangle:

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