Crystal Prism
Posted in Home Treasures on 11/19/2009 06:06 pm by staff
Mega easy question in the area of the surface?
There is this piece of glass, with 2 square pyramids right at both ends of a height prism.The the whole crystal is 54cm.Side the square of the pyramid is 16 cm and height of the prism but it seems more cuboid) is 24cm.Find the surface. Well, basically the diagram composed of a parallelepiped with 2 pyramids at the ends.
Assuming the two pyramids are identical, their height is common (54-24) / 2 = 15 cm We need the height of a triangular side of the pyramids. Look at the picture on this page reference: http://mathworld.wolfram.com/SlantHeight.html We know that h = 15, and R is half the side of the square, so r = 8. By the Pythagorean theorem, s ² = h ² + r ² = 225 + 64 = 289 s = 17 for the area of a triangle = ½ (base) (height) = ½ * 16 * 17 = 136 cm ² There are 8 of these triangles, so its total area = 1088 cm ² The lateral area of the prism is composed 4 rectangles that are each 24 cm × 16 cm, so the total area of these rectangles is 4 * 24 * 16 = 1536 cm ² Therefore, the total area is 1088 + 1536 = 2624 cm ²
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