Question

Find the area of a conves pentagon when area of 4 triangles is unity

Answer 1

A given convex pentagon ABCD has the property that the area of each of the five triangle.
abc
bcd
cde
dea
eab is unity
calculate the area of the pentagon (which need not be regular)
hope it helps you........m

Answer 2

Let ABCDE be a convex pentagon. AB=AE=CD=1.
A
B
=
A
E
=
C
D
=
1.
∠AED=∠ABC=90∘
∠
A
E
D
=
∠
A
B
C
=
90
∘
. DE + BC = 1.

I have very easily shown that area of triangles AED and ABC sum to half into 1/2. But it seems that I am only able to get there. To find the area of triangle ADC I have tried to take its sides in terms of ED but that seems to be too complex. I am stuck.