{"id":42735,"date":"2026-10-21T16:49:54","date_gmt":"2026-10-21T16:49:54","guid":{"rendered":"https:\/\/mp.moonpreneur.com\/math-corner\/?p=42735"},"modified":"2026-10-21T16:51:22","modified_gmt":"2026-10-21T16:51:22","slug":"shape-with-ten-sides","status":"publish","type":"post","link":"https:\/\/mp.moonpreneur.com\/math-corner\/shape-with-ten-sides\/","title":{"rendered":"What Is a Shape with Ten Sides? | Decagon"},"content":{"rendered":"\t\t
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\r\n \r\n <\/div>\r\n\r\n

\r\n <\/strong>\r\n <\/p>\r\n\r\n

\r\n Pick up a pencil and start drawing straight lines that connect end to end until the path closes on itself. Stop at three lines and you have a triangle. Four gives a square or rectangle. Keep going until you have counted ten, and something special appears: a shape with ten sides. It looks almost like a circle in disguise, yet every edge is crisp and straight.\r\nSo what is it, what is it called, and why do mathematicians, designers and scientists find it so fascinating? Let's find out.\r\n<\/span>\r\n <\/div>\r\n\r\n

\r\n \r\n <\/p>\r\n\r\n<\/div>\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t

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\r\n What Is a Shape with Ten Sides Called?\r\n\r\n<\/h2>\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t
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If you have ever wondered <\/span>what is a shape with ten sides called, the answer is a <\/span>decagon.<\/span><\/span><\/p>

The <\/span>name of the shape with ten sides comes straight from ancient Greek. <\/span>Deka<\/span><\/i> means “ten” and <\/span>gonia<\/span><\/i> means “angle” or “corner.” Put them together and you get “ten angles.” Since every corner of a closed polygon comes with a side, a decagon always has ten sides, ten vertices (corners) and ten interior angles.<\/span><\/span><\/p>

That Greek naming habit runs through all of geometry. <\/span>Penta<\/span><\/i> gives us the pentagon (five), <\/span>hexa<\/span><\/i> the hexagon (six) and <\/span>octo<\/span><\/i> the octagon (eight). The decagon simply continues the family tradition.<\/span><\/span><\/p>\t\t\t\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t

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\r\n \r\n <\/polygon>\r\n <\/circle>\r\n <\/svg>\r\n <\/div>\r\n
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Geometry Quick Guide<\/p>\r\n

The Quick Facts: A Decagon at a Glance<\/h3>\r\n <\/div>\r\n <\/div>\r\n\r\n

\r\n Before we go deeper, here's a snapshot of a shape with ten sides<\/strong>.\r\n <\/p>\r\n\r\n

\r\n \r\n \r\n \r\n \r\n \r\n \r\n \r\n \r\n \r\n \r\n
Property<\/th>\r\n Value<\/th>\r\n <\/tr>\r\n <\/thead>\r\n
Number of sides<\/td>\r\n 10<\/td>\r\n <\/tr>\r\n
Number of vertices<\/td>\r\n 10<\/td>\r\n <\/tr>\r\n
Sum of interior angles<\/td>\r\n 1,440\u00b0<\/td>\r\n <\/tr>\r\n
Each interior angle (regular decagon)<\/td>\r\n 144\u00b0<\/td>\r\n <\/tr>\r\n
Each exterior angle (regular decagon)<\/td>\r\n 36\u00b0<\/td>\r\n <\/tr>\r\n
Number of diagonals<\/td>\r\n 35<\/td>\r\n <\/tr>\r\n <\/tbody>\r\n <\/table>\r\n <\/div>\r\n\r\n
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\r\n \ud83d\udca1 Remember:<\/strong> The word \u201cregular\u201d<\/strong> matters! A regular decagon has ten equal sides and ten equal interior angles, while an irregular decagon does not.\r\n <\/p>\r\n <\/div>\r\n\r\n<\/div>\r\n\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t

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\r\n Regular vs. Irregular Decagons\r\n\r\n<\/h2>\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t
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Not every decagon looks the same. Geometry sorts them into two main camps.<\/span><\/p>

Regular decagon:<\/b> All ten sides are equal in length and all ten angles are equal. This is the tidy, symmetrical version most people picture. It has ten lines of symmetry and looks beautifully balanced.<\/span><\/span><\/p>

Irregular decagon:<\/b> The sides and angles can be any mix of sizes, as long as there are ten straight sides forming a closed shape. Think of a stretched, squashed or lopsided version. It is still a decagon, just a free-spirited one.<\/span><\/span><\/p>

There is also a third idea worth knowing: decagons can be <\/span>convex (all corners point outward) or <\/span>concave (at least one corner dents inward, like a cave).<\/span><\/span><\/p>\t\t\t\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t

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\r\n \r\n <\/polygon>\r\n <\/path>\r\n <\/svg>\r\n <\/div>\r\n
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Geometry Made Simple<\/p>\r\n

The Math Behind the Shape<\/h3>\r\n <\/div>\r\n <\/div>\r\n\r\n

\r\n You don't need to be a math whiz to enjoy this part. A few simple formulas unlock almost everything about a decagon.\r\n <\/p>\r\n\r\n

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\r\n \u2220<\/span>\r\n

1. Sum of Interior Angles<\/h4>\r\n <\/div>\r\n

\r\n Any polygon with n<\/em> sides has interior angles that add up to (n \u2212 2) \u00d7 180\u00b0<\/strong>. For ten sides:\r\n <\/p>\r\n

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Formula in action<\/div>\r\n
(10 \u2212 2) \u00d7 180\u00b0 = 1,440\u00b0<\/div>\r\n <\/div>\r\n

\r\n In a regular decagon, divide that by ten and each angle is 144\u00b0<\/strong>. That's wider than the 135\u00b0 angle of an octagon, which helps explain the decagon's broad shape.\r\n <\/p>\r\n <\/div>\r\n\r\n

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\r\n \u2733<\/span>\r\n

2. Counting Diagonals<\/h4>\r\n <\/div>\r\n

\r\n A diagonal connects two corners that are not neighbors. The formula is n(n \u2212 3) \u00f7 2<\/strong>, so:\r\n <\/p>\r\n

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Number of diagonals<\/div>\r\n
10 \u00d7 7 \u00f7 2 = 35 diagonals<\/div>\r\n <\/div>\r\n

\r\n Draw them all inside a regular decagon and you'll get a fascinating web of crossing lines.\r\n <\/p>\r\n <\/div>\r\n\r\n

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\r\n \u25b1<\/span>\r\n

3. Area of a Regular Decagon<\/h4>\r\n <\/div>\r\n

\r\n If each side has length a<\/em>, the area is:\r\n <\/p>\r\n

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Area formula<\/div>\r\n
\r\n Area = (5\/2) \u00d7 a\u00b2 \u00d7 \u221a(5 + 2\u221a5)\r\n <\/div>\r\n
\u2248 7.694 \u00d7 a\u00b2<\/div>\r\n <\/div>\r\n

\r\n For example, a regular decagon with sides of 2 cm has an area of approximately 30.8 cm\u00b2<\/strong>.\r\n <\/p>\r\n <\/div>\r\n\r\n

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\r\n Math takeaway:<\/strong> A decagon has 10 sides, 1,440\u00b0 in total interior angles, 35 diagonals, and an area that depends on its side length.\r\n <\/p>\r\n <\/div>\r\n\r\n<\/div>\r\n\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t

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\r\n A Secret Link to the Golden Ratio\r\n<\/h2>\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t
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Here is the part that makes mathematicians smile. The regular <\/span>shape with ten sides is deeply connected to the <\/span>golden ratio,<\/strong> that famous number of roughly 1.618 that shows up in art, nature and architecture.<\/span><\/span><\/p>

In a regular decagon, the distance from the center to any corner (the circumradius) equals the side length multiplied by the golden ratio. This tight relationship is also why the decagon sits so comfortably alongside the pentagon. Connect every other corner of a decagon and you get two interlocking pentagons. Ancient Greek geometers knew this, and it is one reason the regular decagon can be constructed using nothing more than a compass and a straightedge.<\/span><\/p>\t\t\t\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t

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Recommended Reading:<\/strong><\/p>