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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You are watching: What is the area of a decagon

What is the Area that Decagon?
2.How to find the Area the Decagon?
3.What is the Formula because that Area of Decagon?
4. FAQs top top Area that Decogon

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

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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.