Find the perimeter of the following shape

Question

Consider the following shape:

So i extended a line to form a large equilateral trinagle, which also forms a parallelogram on the left side.

According to the properties of a parallelogram, the side on top should also be 5cm, however, how can i figure out the width?

I thoughout of drawing a line that cuts the 120 angle in half or drawing a 90 degree angle, however none worked.

Please help me find the perimeter of the parallelogram.

Answer 1

The sum of the two sides on the left is $12$ and the top side has length $5+12$.l, which you can see if you extend the left side of the equilateral triangle.

Answer 2

In diagram on extending FD we have equilateral triangle CEF as F = 60 degree, E = 60 degree so angle C is also 60 degree.

So CE = CF = EF = 12 cm

And we have ABCD is a parallelogram. As sum of angle A and B is 180 degree.

BD = AC = 5 cm

Also,

CF = 12 cm

CD + FD = 12 cm

But CD = AB.

Then AB + FD = 12 cm

Perimeter = AB + FD + BD + EF + CE + AC

= 12 + 5 + 12 + 12 + 5 = 46 cm.