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 $3$ $3$ , its base's sides have lengths of $7$ $7$ , and its base has a corner with an angle of $\frac{5 π}{6}$ $(5 pi)/6$ . What is the pyramid's surface area?

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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 $3$ $3$ , its base's sides have lengths of $7$ $7$ , and its base has a corner with an angle of $\frac{5 π}{6}$ $(5 pi)/6$ . What is the pyramid's surface area?

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Answer 1 · 2018-06-30T05:56:40

$A_{p} = A_{b} + L S A = 24.5 + 64.54 = 89.04$ $color(purple)(A_p = A_b + L S A = 24.5 + 64.54 = 89.04$ sq units

Explanation:

Pyramid’s Surface Area $A_{p} = A_{b} + L S A$ $A_p = A_b + L S A$

where $A_{b} = s^{2} sin θ, L S A = 4 \cdot (\frac{1}{2}) s \sqrt{{(\frac{s}{2})}^{2} + h^{2}}$ $A_b = s^2 sin theta, L S A = 4 * (1/2) s sqrt((s/2)^2 + h^2)$

Given $s = 7, h = 3, θ = \frac{5 π}{6}$ $s = 7, h = 3, theta = (5pi)/6$

$A_{b} = 7^{2} \cdot sin (\frac{5 π}{6}) = 24.5$ $A_b = 7^2 * sin ((5pi)/6) = 24.5$

$L S A = 4 \cdot (\frac{1}{2}) \cdot 7 \cdot \sqrt{{(\frac{7}{2})}^{2} + 3^{2}} \approx 64.54$ $L S A = 4 * (1/2) *7 * sqrt((7/2)^2 + 3^2) ~~ 64.54$

$A_{p} = A_{b} + L S A = 24.5 + 64.54 = 89.04$ $color(purple)(A_p = A_b + L S A = 24.5 + 64.54 = 89.04$ sq units

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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 $3$ $3$ , its base's sides have lengths of $7$ $7$ , and its base has a corner with an angle of $\frac{5 π}{6}$ $(5 pi)/6$ . What is the pyramid's surface area?

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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 33 , its base's sides have lengths of 77 , and its base has a corner with an angle of 5π6(5 pi)/6 . What is the pyramid's surface area?

1 Answer

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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 $3$ $3$ , its base's sides have lengths of $7$ $7$ , and its base has a corner with an angle of $\frac{5 π}{6}$ $(5 pi)/6$ . What is the pyramid's surface area?