A museum exhibit, ABCD, has infrared beams around it for security, as shown below.If the length of the beams is made six times the original length on each side, which statement is correct about the maximum area available for an exhibit to be displayed?
it becomes 12 times the original area.
It becomes 18 times the original area.
It becomes 36 times the original area.
It becomes 54 times the original area.

Question

A museum exhibit, ABCD, has infrared beams around it for security, as shown below.If the length of the beams is made six times the original length on each side, which statement is correct about the maximum area available for an exhibit to be displayed?
                it becomes 12 times the original area.
		It becomes 18 times the original area.
		It becomes 36 times the original area.
		It becomes 54 times the original area.

happykiddo · Answer

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happykiddo · Answer

please help if your reading this

dominusscholae · Answer

The parallelogram here is a trapezoid. Thus the area of this parallelogram is: $$(b1+b2)h/2$$. In this case, b1 = AB and b2 = CD. and the height (h) is AD. When each length is timed by six, the new sides are just 6 times the original length of each. Plugging this in, the new area is: $$1/2(6h(6b1+6b2), or (after factoring), 36(1/2(b1+b2)h)$$ . Since the original area is 1/2(b1+b2)h, the new area is just 36 times the original area.