angelaOR
02.09.2019 •
Mathematics
The pyramid shown has a square base that is 18 inches on each side. it has a surface area of 864 square inches. what is the slant height?
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Ответ:
the slant height is 15 inches.
let s be the slant height
surface area of a square base pyramid is
sa = area base + 4 * (area of slant triangle)
the area of a slant triangle is 1/2 * (base length) * (slant height) so
sa = area base + 4 · [ 1/2 * (base length) · (slant height) ]
sa = area base + 2 · (base length) · (slant height)
the (area base) is equal to 18in · 18in = 324in²
the (base length) is given in the question as 18
the sa is equal to 864
we can use this information to solve for (slant height), s
864 = 324 + 2 · 18 · (slant height)
540 = 2 · 18 · (slant height)
540 = 36 · (slant height)
slant height = 15
the slant height is 15 inches.
Ответ: