- posted
14 years ago

Well don't say I didn't try to give you a hint. The spars consist of triangles, all facing the same way and with their bases touching each other. To find the total area of metal in the triangles in each of the three cases. Area of each triangle = 1/2 base x height. As the bases touch then the sum of the base length is the length of the beam - in all three cases. The height is the depth of the beam - in all three cases. Therefore the total area of metal = 50% of the cross sectional area of the beam - in all three cases.

It doesn't matter what shape the triangles are in such an arrangement. The area will always be half that of the beam. The triangles can even be non symmetrical without affecting the solution and in fact it still doesn't matter if they aren't all the same shape.