The answer to the question “what shape has 5 sides and 5 vertices” is shown below: In the Geometry, a type of Polygon which has 5 sides and 5 vertices is known as pentagon. Now here we will see some properties of pentagon:

Interior angle - 108 degree is the interior angle of a pentagon. Now the formula for finding the interior angle of a pentagon:

The formula for finding the interior angle is:

Interior angle = (180n – 360)/n,

Where, the value of ‘n’ is the number of sides in a pentagon. So the number of sides in a pentagon is 5; because pentagon has five sides and five vertices.

Exterior angle – 72 degree is the exterior angle of a pentagon. A linear pair is formed with the interior angle of a pentagon. The formula for finding the exterior angles of a pentagon is:

Exterior angle = (180 – interior angle),

Area – 1.72 s^{2} approximately is the area of a pentagon,

Where‘s’ represents the length of a side, now we find the area of a pentagon when length of side is given:

Area = __s ^{2}N,__

4tan (180/N)

Where, ‘s’ represents the length of any side of a pentagon.

‘N’ is the number of sides in a pentagon.

‘Tan’ is used for finding the Tangent function.

When the radius of a pentagon is given then the formula for finding the area of a pentagon is:

Area = __R ^{2}Nsin (360/N),__

2

Where, ‘r’ represents the radius,

‘N’ denotes the number of sides in a pentagon,

And ‘sin’ is the trigonometric function which is calculated in degrees.

And if in radius or apothem of a pentagon is given then the formula is:

Area = M^{2}Ntan (180/N),

Where, ‘M’ is the length of the apothem or inradius of a pentagon.