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 $1$ , its base's sides have lengths of $7$ , and its base has a corner with an angle of $( pi)/4$ . What is the pyramid's surface area?

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Answer 1 · 2018-04-29T03:45:05

$color(indigo)(T S A = A_T = 34.65 + 50.96 = 85.61 " sq units"$

https://socratic.org/questions/a-pyramid-has-a-base-in-the-shape-of-a-rhombus-and-a-peak-directly-above-the-bas-34

$l = 7, h = 1, theta = pi/4, " To find surface area of pyramid"$

$"Area of base " A_b = l^2 sin theta = 7^2 * sin (pi/4) = 34.65$

$"Slant height of pyramid " s = sqrt(h^2 + (l/2)^2) = sqrt(1^2 + (7/2)^2) = 3.64$

$"Lateral Surface Area of Pyramid " A_l = 4 * (1/2) * l * s$

$L S A = A_s = 4 * (1/2) * 7 * 3.64 = 50.96$

$"Total Surface Area " = T S A = A_T = A_b + A_s$

$color(indigo)(T S A = A_T = 34.65 + 50.96 = 85.61 " sq units"$

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 1 1 , its base's sides have lengths of 7 7 , and its base has a corner with an angle of ( pi)/4 ( pi)/4 . What is the pyramid's surface area?