How To Find The Area Of A Decagon
The expanse of a decagon is defined equally the number of unit of measurement squares that tin can be fit within it. Decagons as shapes are effectually usa in the grade of coins, watches, designs, and patterns. A decagon is a ii-dimensional, ten-sided polygon. The give-and-take is fabricated up of "deca" and "gon" where "deca" means x and "gon" means sides. In this lesson, we volition discuss the concept of the area of a decagon and learn to make up one's mind the area of a decagon using examples. Stay tuned to learn more!!!
| 1. | What is the Area of Decagon? |
| 2. | How to Notice the Area of Decagon? |
| 3. | What is the Formula for Area of Decagon? |
| 4. | FAQs on Surface area of Decogon |
What is Area of Decagon?
The area of the decagon is the amount of region it covers. A decagon is a plane figure with 10 sides. It has 10 interior angles. A regular decagon has all its 8 sides and eight interior angles equal. And then, for a regular decagon with x sides, we can draw 35 diagonals and it has ten vertices. Since the sum of all the interior angles of a decagon is 1440°, the value of each interior bending for a regular decagon is 144°. The sum of all the exterior angles of a regular decagon is 360°. The unit of expanse of decagon can be given in terms of mii, cmtwo, intwo or ftii.
How to Find the Area of Decagon?
A regular decagon is divided into ten congruent isosceles triangles when all its diagonals are drawn. Therefore, the area of a decagon is given every bit, area of a decagon = area of 10 congruent isosceles triangles and then formed
⇒ Area of a decagon = 10× Area of each coinciding isosceles triangle
We tin find the expanse of a decagon using the post-obit steps:
- Stride 1: Find the area of each congruent isosceles triangle.
- Step 2: Multiply the value of the surface area of each congruent isosceles triangle past 10.
- Step 3: Write the unit of measurement in the cease, once the value is obtained.
What is the Formula of the Expanse of Decagon?
Let'due south use the fact that the area of a decagon is equal to the surface area of the 10 isosceles triangles formed in a decagon when diagonals are drawn. Therefore,
⇒ Area of a decagon = 10× Expanse of each congruent isosceles triangle
Let'due south first detect the area of each isosceles tringle first:
Area of each isosceles triangle = ane/2 × Base × Elevation
⇒ Area of each isosceles triangle = 1/2 × a × h
Height of the isosceles triangle, h = a/two × tan 72° = a/2 ×\({ \ \sqrt{ten+2\sqrt{5}} \over \sqrt{5}-1}\)
⇒ Area of each isosceles triangle = 1/ii × a × a/2 ×\({ \ \sqrt{10+2\sqrt{5}} \over \sqrt{five}-1}\)
⇒ Area of each isosceles triangle = atwo/iv ×\({ \ \sqrt{10+two\sqrt{v}} \over \sqrt{five}-ane}\)
Substituting the value, nosotros get:
Area of a decagon = ten× a2/four ×\({ \ \sqrt{10+two\sqrt{5}} \over \sqrt{5}-i}\)
⇒ Surface area of a decagon = 5atwo/2 ×\({\sqrt {20 + 8\sqrt{5} \over 4}}\)
= 5a2/2 ×\({\sqrt {5 + two\sqrt{5}}}\)
Therefore, the formula for the area of a decagon is 5a2/2 ×\({\sqrt {5 + 2\sqrt{v}}}\). So if nosotros know the value of the side length of a regular octagon we can hands find its surface area.
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FAQs on Area of a Decagon
How Many Sides Are At that place in a Decagon?
The give-and-take decagon is made of two words "deca" and "gon", where the word "deca" refers to x and "gon" refers to sides. Thus, there are 10 sides in a decagon.
How Can We Notice the Area of a Decagon?
We tin can find the area of the decagon using the post-obit steps:
- Pace 1: Detemine the surface area of each congruent isosceles triangle.
- Step 2: Now, multiply the value of the area of each congruent isosceles triangle by x.
- Step 3: Once the value of the area of the decagon is obtained, write the unit in the end.
What is the Formula to Detect the Surface area of a Regular Decagon?
The formula to make up one's mind the value of the area of a decagon is 5aii/ii ×\({\sqrt {5 + 2\sqrt{v}}}\), where 'a' is the side length of the decagon.
What Are the Units Used for the Area of a Decagon?
The unit of 'surface area' is "square units". For example, it tin be expressed equally thousand2, cmii, in2, etc depending upon the given units.
How to Find the Area of Decagon If the Area of an Isosceles Triangle Formed Past Its Diagonal is Known?
Nosotros can determine the area of decagon if the expanse of an isosceles formed by its diagonal is known using the following steps:
- Footstep 1: Write the dimension of the expanse of an isosceles triangle formed.
- Step 2: Determine the expanse of the decagon using the formula area of a decagon = 10 × area of each congruent isosceles triangle.
- Step 3: Once the value of the area of the decagon is obtained, write the unit of measurement in the finish.
What Happens to the Surface area of Regular Decagon If the Length of the Side of Decagon is Doubled?
The surface area of a regular decagon quadruples if the length of the side of the decagon is doubled equally "a" in the formula gets substituted by "2a". Thus, A = 5(2a)two/2 ×\({\sqrt {5 + 2\sqrt{five}}}\) = iv (5aii/2 ×\({\sqrt {v + 2\sqrt{5}}}\)) which gives four times the original value of the area.
What Happens to the Area of Regular Decagon If the Length of the Side of Decagon is Halved?
The area of a regular decagon becomes one-fourth if the length of the side of the decagon is halved as "a" in the formula gets substituted by "a/2". Thus, A = 5(a/two)ii/2 ×\({\sqrt {5 + 2\sqrt{five}}}\) = (one/4) × (5a2/two ×\({\sqrt {v + 2\sqrt{five}}}\)) which gives 1-fourth the original value of the area.
Source: https://www.cuemath.com/measurement/area-of-decagon/
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