A square pyramid is 8 m on each side. The surface area is 240 m2. What is the slant height
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A square pyramid is 8 m on each side. The surface area is 240 m2. What is the slant height

[From: ] [author: ] [Date: 12-08-13] [Hit: ]
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Please help

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Is 240 the total surface area or the surface area of the lateral faces ??

If 240 the area of the 4 triangles:

60 = area of one triangle = 1/2*b*h where the base is 8 and the height is the slant height of the pyramid

120 = b*h
h = 120/b
h = 120/8 = 15 m
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If 240 the TOTAL surface area:

240 - 64 = 176, the area of 4 triangles

176/4 = area of one triangle with base = 8

44 = 1/2*b*h

88 = b*h

h = 88/b

h = 88/8 = 11 m

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[Base Area] + 1/2 × Perimeter × [Slant Length], base area = 8 X 8 = 64m2

64m2 + 1/2 * 8m + 8m + 8m + 8m × [Slant Length] = 240m2

64m2 + 1/2 * 32m * [Slant Length] = 240m2

64m2 + 16m * [Slant Length] = 240m2

16m * [Slant Length] = 176m2

[Slant Length] = 176m2 / 16m = 11m

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Let the slant height be h:
(8h)(4)/2 + 64=240
h=176/16= 11 m
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