A pyramid has a base in the shape of a rhombus and a peak directly above the base's center. The pyramid's height is $7$ , its base's sides have lengths of $2$ , and its base has a corner with an angle of $(7 pi)/8$ . What is the pyramid's surface area?

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Answer 1 · 2018-07-23T09:55:52

Surface area of the pyramid $T S A = 29.815$ sq. units.

Pyramid surface area = base area + lateral Surface area.

i. e. $T S A = A_b + L S A$

$A_b = 2^2 sin ((7pi)/8) = 1.5307$ sq. units

Height of pyramid $= 7$

Slant height of lateral surface $s = sqrt((2/2)^2 + 7^2) = sqrt 50$

$L S A = 4 * ((1/2) * 2 * sqrt50) = 28.2843$ sq. units.

$T S A = A_b + L S A = 1.5307 + 28.2843 = 29.815$ sq. units.

A pyramid has a base in the shape of a rhombus and a peak directly above the base's center. The pyramid's height is 7 7 , its base's sides have lengths of 2 2 , and its base has a corner with an angle of (7 pi)/8 (7 pi)/8 . What is the pyramid's surface area?