# Find area of irregular polygon [closed]

I am currently taking the Scottish Mathematical Council's Mathematical Challenge 2016/17. I am unable to solve problem S4.

For this problem, I need to find the area of this irregular polygon.

I have attempted to split it up into smaller shapes (triangles and rectangles) but am still unable to solve it.

## closed as off-topic by Silvia Ghinassi, iadvd, Ethan Bolker, Shailesh, LeucippusSep 28 '16 at 1:13

This question appears to be off-topic. The users who voted to close gave this specific reason:

• "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – Silvia Ghinassi, iadvd, Shailesh, Leucippus
If this question can be reworded to fit the rules in the help center, please edit the question.

Show that the right vertex and the left vertex are at the same height, and that the top vertex is $\frac12$ above them. Then we can split the shape into
• a $1\times 1$ square
• a right triangle with legs $1$ and $\sqrt 3$
• a triangle with base $1+\sqrt 3$ and height $\frac12$
$$S = \frac{1}{2}(1)(1) + \frac{1}{2}\sqrt{2}\sqrt{3}\sin(75) + \frac{1}{2}(1)(2)\sin(60)$$