Pentagon's Area.?

Question

How do you calculate the area of a pentagon?
Thanks =]

Answer 1

OK, you divide the pentagon into 3 triangles and find the area
of each and add them, but how.
You must have the lengths of the sides and the angles between
them. Then label the vertices of of the pentagon A,B,C,D,E. Draw lines AC and AD. Now you have 3 triangles, ABC, ACD and ADE. Compute the length of AC. You have the lengths of the
sides and the included angle known. You compute that with the
law of cosines. { In a triangle with sides P,Q and R, where
P and Q are known and the included angle between them(r)
also known, then R^2=P^2+Q^2-2PQcos(r) }.
Compute the length of AD similarly.
Now the area of ABC is (1/2)(AB)h where h=ABsinB.
Similarly the area of ADE is (1/2)(AE)h where h=AEsinE.
All three sides of triangle ACD are known but no angles are
known. So use the the sin law and we get
sin(BAC)=(BCsinB)/AC and sin((EAD)=(DEsinE)/AD.
Angle CAD=A -BAC-EAD.
Area of CAD= (1/2)(AC)h where h=ACsin(angleCAD).

Answer 2

The area of a pentagon is equal to five times the area of its composing triangles. The area of a triangle is (1/2)*b*h (b and h are the ones of each triangle), so, the area of the pentagon shall be (5/2)*b*h.

Answer 3

1) Divide the pentagon into five triangles, calculate the area of each one:

A = 1/2 bh

Where b is the base of a triangle and h is height

2) Add the five areas.

*** If it is regular, all the sides of the pentagon are the same, all the triangles are equal and it comes to:

A = 5 * 1/2 * b * h = 1/2 perimeter * h = perimeter * apothem / 2

5 * b = perimeter

h = height of triangle = apothem

A perpendicular from the center of a regular polygon to one of its sides is called apothem.

Try to do it for a regular hexagon.

Answer 4

You need to divide the pentagon into 5 separate triangles and then calculate the area of each of the triangles (1/2bh)

Answer 5

Equals 5 times the area of the triangle delimited by one side and the 2 lines joining its center to each vertex.
You are brought back to calculating the area of a triangle, which is half the side times its related height