Area calculator | 16 popular shapes! (2023)

There are many useful formulas to calculate the area of easier forms. In the following sections you will not only find the known formulas for triangles, rectangles and circles, but also other forms such as parallelograms, dragons or annuli.

We hope that, according to this explanation, you have no problems define what kind of area is in mathematics!

Well, of course itdepends on the shape! In the following you will find formulas for all sixteen forms that are presented in our area calculator. In addition to the reason of clarity, we will only list the equations - their images, explanations and derivations can be found in the following separate paragraphs (and also in tools that everyoneare devoted to certain form).

Are you ready? Here are the most important and useful area formulas for sixteen geometric forms:

• SquareArea formula:A = a²
• rectangleArea formula:A = a × b
• triangleArea formulas:
  • A = B × H / 2or
  • A = 0,5 × A × B × sin (γ)or
  • A = 0,25 × √ ((a + b + c) × (-a + b + c) × (a - b + c) × (a + b - c)))or
  • A = a² × sin (b) × sin (c) / (2 × sin (b + c))
• KreisArea formula:A = πr²
• Circular sectorArea formula:A = R² × shop / 2
• EllipseArea formula:A = a × b × p
• trapezeArea formula:A = (a + b) × h / 2
• ParallelogrammArea formulas:
  • A = a × hor
  • A = a × b × sin (Winkel)or
  • A = e × f × sin (store)
• RhombusArea formulas:
  • A = a × hor
  • A = (e × f) / 2or
  • A = S² × Sin (store)
• KiteArea formulas:
  • A = (e × f) / 2or
  • A = a × b × sin (γ)
• PentagonArea formula:A = a² × √ (25 + 10√5) / 4
• HexagonArea formula:A = 3/2 × √3 × a²
• octagonArea formula:A = 2 × (1 + √2) × a²
• AnnulusArea formula:A = π (R² - R²)
• squareArea formula:A = e × f × sin (store)
• Regular polygonArea formula:A = n × a² × cot (π / n) / 4

Would you like to change the area unit? Just click on the unit name and a dropdown list is displayed.

Have you forgot how high the Square area is? Then you are in the right place. The area of a square is the product of the length of its pages:

• Square surface = a × a = a², WoAIs a square side

This is the most basic and most common formula, although others also exist. For example, there are square surface formulas that use diagonal, scope, circradius or inradius.

The formula for the rectangular area is also a child's play - it is simply the multiplication of the rectangular pages:

• Rectangular area = a × b

The calculation of the rectangular area is extremely useful in everyday situations: from Baubau (estimate of the tiles, decks, siding or finding the roof area) to the decoration of your apartment (how much color or wallpaper do I need?) To calculate your yoursPeople are cake.

1. Given base and height

• Triangular area = W / 2

2. Two pages and the angle between them (SAS)

• Triangular surface = 0.5 × a × W × sin (γ)

3. Three pages (SSS)(This triangle area formula meansHerons Formel)

• Dreieckfläche = 0,25 × √ ((a + b + c) × (-a + b + c) × (a - b + c) × (a + b - c)))

You can discover more in theHerons Formel Rechner.

4. Two angles and the side between them (ASA)

• Triangular area = a² × sin (b) × sin (c) / (2 × sin (b + c))

There is a special type of triangle, the right triangle. In this case, the basis and the height are the two sides that form the right angle. Then the area of a right triangle can be expressed as:

Right triangle area = a × b / 2

The circle area formula is one of the best known formulas:

• District area = πR², WoRIs the radius of the circle

In this calculator we only implemented this equation, but in ourDistrict computerYou can calculate the area from two different specified formulas:

1. diameter

• Circular area = πR² = π × (d / 2) ²

2. Scope

• District area = c² / 4π

In addition, the Circle Area formula is useful in everyday life -like the serious dilemma for which the pizza size must be chosen.

The sector area formula can be accepted by taking a circle. The area of the sector is proportional to its corner.Therefore we can write that:

α / 360 ° = sector area / district area

Angle conversion tells us that360 ° = 2p

A / 2p = sector surface / pr²

So:

• Sector surface = R² × α / 2

To find an ellipse area formula, first remember the formula for the area of a circle:πr²For an ellipse you have no value for the radius, but two different values:AAndB. The only difference between the circle and the formula of the ellip surface is the substitution ofr²Through the product of the semi-major and semi-minor axes,a × b:

• Ellipsisfish of space = π × A × B

The area of a trapezoid can be found according to the following formula:

• Trapeze area = (a + b) × h / 2, WoAAndBAre the lengths of the parallel sides andHIs the height

In addition, the formula of the trapezoidal area can be expressed as:

Trapeze area = M × H, WoMIs the arithmetic mean of the lengths of the two parallel sides

1. Base and height

• Parallelogrammbereich = a × h

2. pages and an angle between them

• Parallelogram surface = a × b × sin (a)

3. Diagonal and an angle between them

• Parallelogram surface = e × f × sin (θ)

1. Page and height

• Rhombusbereich = a × h

2. diagonal

• Rhombus surface = (E × F) / 2

3rd page and every angle, e.g.B. α

• Rhombus area = a² × sin (a)

To calculate the area of a kite, two equations can be used, depending on what is known:

1. area of a kite formula with kite diagonal

• Dragon area = (E × F) / 2

2. area of a kite formula, in two non-controlling side lengths and the angle between these two sides

• Kite area = a × b × sin (α)

The area of a pentagon can be calculated from the formula:

• Pentagon area = a² × √ (25 + 10ond) / 4, WoAis a side of a normal pentagon

Take a look at our committed onesPentagon calculator, where other essential properties of a regular pentagon are provided: page, diagonal, height and scope as well as the radius of the meter and the Incircle.

The basic formula for the area of a hexagon is:

• Six canteen = 3/2 × √3 × a²where A is the regular hexagon side

Where does the formula come from? You can imagine a regular hexagon as the collection of six congruent triangles. To find the hexagon area, we only have to find the area of a triangle and multiply it. The formula for a regular triangle area corresponds to the square areaSide of the square root of 3 divided by 4:

Equal triangular area = (a² × √3) / 4

Six canteen = 6 × equilateral triangular range = 6 × (a² × √3) / 4 = 3/2 √3 × a²

To find the Octagon area, all you have to do is know the side length and the following formula:

• Oktagon surface = 2 × (1 + √2) * a²

The Octagon area can also be calculated from:

Oktagon surface = perimeter × apothem / 2

A radius in the Octagon case is easy8 × a. And what is an apothem? An apothem is a distance from the middle of the polygon to the center of a side. At the same time it is the height of a triangle that takes a line from the corner points of the octagon to its center. This triangle - one of eightCongruent - is an Iszelic triangle, so its height can be calculated from the formula using Pythagoras' theorem:

H = (1 + √2) × a / 4

Finally we get the first equation:

Actagon surface = circumference * apothem / 2 = (8 × a × (1 + √2) × a / 4) / 2 = 2 × (1 + √2) × a²

A annulus is a ring-shaped object-ES is a region that is limited by two concentric circles of different radii. Finding the area of an annulus formula is an easy task if you remember the formula of the district area.Annulus area is a difference in the areas of the larger radius -R circle and the smaller radius r:

• Annulus area = Pr² - Pr² = π (R² - R²)

The square formula, which implemented this area, uses two given diagonal and the angle between them.

• Square area = e × f × sin (α), WoeAndFare diagonals.

We can use two angles if we calculate your sinus. If we know that two neighboring angles are complementary, we can say thatSin (angle) = sin (180 ° - angle).

If you are looking for other formulas for the area of a square, you will see our committed onesSquare calculatorwhere you can find the formula of Bretschneider (with four sides and two opposite angles) and a formula that Bimedians uses and the angle between them.

The formula for the regular polygon range looks like this:

• Regular polygon surface = n × a² × cot (π / n) / 4

Where n is the number of pages and a the side length.

There are other equations and use z.B. parameters such as circrad radius or scope. They can find these formulas in a special paragraph from ourPolygon surface calculator.

If you have to do with an irregular polygon, remember that you always in simpler figures, e.g.B. triangles, can simply be divided. Simply calculate the area of each of them and summarize them at the end.

Calculation of the area of an irregular form:

1. Share the shape into several subhapes, for which you can easily carry out the surface calculations, such as triangles, rectangles, trapezoids, (half) circles, etc.
2. Calculate the area of each of these subhapes.
3. Summarize the areas of the undercuts to achieve the end result.