SOLUTION: A pentagon is formed by a rectangle and an equilateral triangle (external to it)with the side (of the triangle) in common with a dimension of the rectangle. Knowing that one dimens

Algebra ->  Formulas -> SOLUTION: A pentagon is formed by a rectangle and an equilateral triangle (external to it)with the side (of the triangle) in common with a dimension of the rectangle. Knowing that one dimens      Log On


   

Question 254096: A pentagon is formed by a rectangle and an equilateral triangle (external to it)with the side (of the triangle) in common with a dimension of the rectangle. Knowing that one dimension of the rectangle measures 4.2 cm and that the diagonal is 7 cm, determine the perimeter and the area of the pentagon.
I just can't figure out the figure. I tried using a square, but it doesn't seem to work right... And it can't be a rectangle because then all the sides of the pentagon would not be egual. I would really appreciate all the help I can get! Thank you!
Answer by edjones(8007) About Me  (Show Source):
You can put this solution on YOUR website!
This is not a regular pentagon. The sides are not equal.
For the sides of the rectangle:
a^+b^2=c^2
a^2+4.2^2=7^2
a^2+17.64=49
a^2=31.36
a=5.6
So the rectangle's sides are 5.6 and 4.2
We can make the sides of the triangle either number; I will use 4.2; you can use 5.6 if you wish.
A=s^2sqrt(3)/4 for an equilateral triangle.
=17.64sqrt(3)/4
=4.41sqrt(3)
5.6*4.2*4.41sqrt(3)=179.7 sq cm Area of pentagon
5.6*2+4.2*3=23.8 cm Perimeter of pentagon.
.
Ed