# Please help me find the area of an irregular shape (a map) having 5 sides.?

I've posted the map at http://www.flickr.com/photos/62717419@N08/57039856...

The sides are 55 ft, 30 ft, 83 ft, 53 ft and 55 ft.

Diagonals are 94 ft and 64 ft.

Any illustration is most welcome. But need the answer in figure.

CORRECTION: The sides are 55 Ft, 30 Ft, 83 Ft, 15 Ft (not 53 Ft as rendered above) and 55 Ft.

Diagonals are the same as above.

### 2 Answers

- norcekriLv 79 years agoFavorite Answer
Starting at the far left, let's label the points ABCDE. Label the diagonal intersection T.

AB = 55, BC = 55, CD = 30, and so on.

Note that you have all three sides for triangles BCD and CDE.

Use the law of cosines to get one angle of each triangle; use the law of sines to get the others.

This allows you to find the angle measures at T. Use the law of sines on triangle TCD to get sides CT and DT. Subtract from the diagonal lengths to get the lengths of TB and TD.

Draw diagonal BE. Use the law of cosines with sides BT, TE, and angle BTE to find its length.

Finally note that you have partitioned the pentagon into triangles ABE, BCE, and CDE, and you know the lengths of all their sides. Use Heron's formula to find the area of each triangle. Add them up, and there's your answer.

Heron's formula:

Source(s): Former math/CS teacher. - picklesimerLv 43 years ago
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