Can anyone tell me the height of this?

http://learn.flvs.net/webdav/assessment_images/educator_geometry_v14/pool_Geom_3641_0810_19/image0034e68d166.jpg

Question

Can anyone tell me the height of this?

http://learn.flvs.net/webdav/assessment_images/educator_geometry_v14/pool_Geom_3641_0810_19/image0034e68d166.jpg

anonymous · Answer

It isn't 8 cm?

anonymous · Answer

Well it states in the whole question that the diameter is 8. I didn't think that I should use it for the height too?

anonymous · Answer

Oh ok. No those are different.

anonymous · Answer

Maybe 12+5... Why else would those be there. See I'm trying to find the surface area of this whole figure.

anonymous · Answer

no not that

anonymous · Answer

height will be 
$$12 + 2*(\sqrt{5^{2}-4^{2}})$$

anonymous · Answer

Why so?

anonymous · Answer

12 is the length of the rectangle.
there are 2 similar triangles on either side of it.
now if you drop a perpendicular bisector on both the sides(of 8cm)from the tips of the triangle and apply Pythagoras theorem you will get the length of the perpendicular bisector as $$\sqrt{5^{2}-4^{2}}$$