The area of a decagon is defined as the variety of unit squaresthat can be fit within it.Decagons as forms are about us in the form of coins, watches, designs, and patterns. A decagon is a 2-dimensional, ten-sided polygon. Words is comprised of "deca" and "gon"where "deca"means ten and also "gon"means sides. In this lesson, us will talk about the concept of the area that a decagon and also learn to determine the area the a decagon making use of examples. Continue to be tuned to discover more!!!

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## What is Area ofDecagon?

The area of the decagon is the lot of region it covers.A decagon is a plane figure v 10 sides. Ithas 10 interior angles. A regular decagon has actually all the 8 sides and 8 interior angles equal. So, for a constant decagon through 10 sides, us can attract 35diagonals andit has 10 vertices. Due to the fact that the sum of all the inner angles that a decagonis 1440°, the worth of each internal angle for a continual decagon is 144°. The sum of every the exterior angle of a constant decagon is 360°. The unit the area the decagon can be provided in regards to m2, cm2, in2 or ft2.

## How to discover the Area the Decagon?

A constant decagon is divided into 10 congruent isoscelestriangles once all that is diagonals room drawn. Therefore, the area of a decagon is given as, area of a decagon = area of 10 congruent isoscelestriangles for this reason formed⇒ Area that a decagon = 10× Area of every congruent isosceles triangle

We can discover the area the a decagon utilizing the adhering to steps:

Step 1: discover the area of each congruent isosceles triangle.Step 2: Multiply the worth of the area ofeach congruent isosceles triangle by 10.Step 3: Write the unit in the end, as soon as the value is obtained.

## What is the Formula that the Area of Decagon?

Let's usage the fact that the area that a decagon is same to the area of the 10 isosceles triangles developed in a decagon when diagonals room drawn. Therefore,⇒ Area that a decagon = 10× Area of each congruent isosceles triangle

Let's first find the area of every isosceles tringle first:

Area of every isosceles triangle = 1/2× Base× Height

⇒Area of each isosceles triangle = 1/2× a× h

Height of the isosceles triangle, h = a/2× tan 72° = a/2×( sqrt10+2sqrt5 over sqrt5-1)

⇒Area of every isosceles triangle = 1/2× a × a/2×( sqrt10+2sqrt5 over sqrt5-1)

⇒Area of every isosceles triangle = a2/4×( sqrt10+2sqrt5 over sqrt5-1)

Substituting the value, we get:

Area the a decagon = 10× a2/4×( sqrt10+2sqrt5 over sqrt5-1)

⇒Area that a decagon = 5a2/2×(sqrt 20 + 8sqrt5 over 4)

=5a2/2×(sqrt 5 + 2sqrt5)

Therefore, the formula because that the area that a decagon is5a2/2×(sqrt 5 + 2sqrt5). Therefore if we know the value of the side length of a consistent octagon we deserve to easily discover its area.

## Examples ~ above Area that Decagon

Example 1:Find the area of a consistent decagon through a side length of 10 cm.

Solution:Given, the side size of a decagon, a = 10 cm

As we know, the area of the decagon =5a2/2×(sqrt 5 + 2sqrt5)

⇒Area that a decagon =5 × 102/2×(sqrt 5 + 2sqrt5)

⇒Area the a decagon = 250×(sqrt 5 + 2sqrt5)≈ 769.42 square units.Therefore, the area that the continuous decagon is769.42 square units.

Example 2: find the area the a regular decagon if the area of among the isosceles triangles created by the diagonals is 9square units.

Solution:Given, the area of one of the isosceles triangles formed by diagonal line is9square units.

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As us know, area that a decagon = 10 × area of every congruent isosceles triangle⇒Area the the decagon = 10× 9⇒Area the a decagon = 90 square unitsTherefore the area that the decagon is90 square units.