Long story short, we are having a High School Geometry test tomorrow, and as I was practicing a came accross a trigonometry task in my textbook, which looked simple, but I couldn't figure out the way to solve it.
The task here is to find the area of the whole polygon. According to the textbook's answer sheet, the answer is 428 square the centimeters (the other values on the image are in centimeters).
I could easily figure out the sides of the bottom 4 triangles with the pythegorian theorem, and their area can be easily calculated with Heron's formula, but I cannot solve the top 2 triangles. I would appreciate if you could give me any help with that.
Area of top triangle: $\dfrac{7\times 28}{2}$ = $7\times 14$ = $98$
Area of middle triangle: $\dfrac{30\times 12}{2}$ = $30\times 6$ = $180$
Area of bottom triangle: $\dfrac{30\times 10}{2}$ = $30\times 5$ = $150$
Adding them together: $428$