Answer :
The goal is to find the area of a pentagon with side length 8.
We can find the area of a pentagon very easily by splitting it up into 10 congruent right triangles with the apothem as the height. The base of one of these triangles would be 4. The base angle would be 54 degrees, because it's half of the angle of a regular pentagon.
Using trig we find that the height of this triangle/apothem of the pentagon is equal to 4tan(54 degrees), which is about 5.506.
The area of a triangle is bh/2, so...4*5.506/2 = 11.011 in².
Times 10 triangles is 110.11 in².
We can find the area of a pentagon very easily by splitting it up into 10 congruent right triangles with the apothem as the height. The base of one of these triangles would be 4. The base angle would be 54 degrees, because it's half of the angle of a regular pentagon.
Using trig we find that the height of this triangle/apothem of the pentagon is equal to 4tan(54 degrees), which is about 5.506.
The area of a triangle is bh/2, so...4*5.506/2 = 11.011 in².
Times 10 triangles is 110.11 in².
