posted by Louisa on .
What is the area of a regular pentagon with a side length of 9.4 feet and an apothem length of 6.5 feet?
asume 11 and 12 are parallel 5 is 83 what is the measure of 7
no sides of a regular pentagon are parallel
5 is not 83
7 is 7
What planet are you calling from?
Divide the pentagon into 5 congruent triangles with base angles of 54°
If s = side length,
the triangles have base = s
then the apothem is h = s/2 tan 54°
The area of the pentagon is 5 * s/2 * s/2 tan 54° = 5s^2*tan54°/4
Note that this is just area = 1/2 * perimeter * apothem
Note: 6.5/4.7 = 1.383 but tan54° = 1.376 so the above dimensions do not fit a regular pentagon.
Ignoring that, however, and using their figures,
a = 5*9.4/2 * 6.5 = 152.75
Erica is playing with some regular pentagon tiles and discovers she can made a five pointed star:Explain how she can use angle measures of the pentagons to fink the angle measure of the point of the star