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 $5$ $5$ , its base's sides have lengths of $9$ $9$ , and its base has a corner with an angle of $\frac{5 π}{8}$ $(5 pi)/8$ . 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 $5$ $5$ , its base's sides have lengths of $9$ $9$ , and its base has a corner with an angle of $\frac{5 π}{8}$ $(5 pi)/8$ . What is the pyramid's surface area?

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Answer 1 · 2018-06-10T05:55:52

$T S A of Pyramid A_{p} = 74.83 + 121.08 = 195.91$ $color(purple)(T S A " of Pyramid " A_p = 74.83 + 121.08 = 195.91$

Explanation:

$S u r f a c e A r e a o f P y r a m i d = A r e a o f ρ m b u s b a s e + A r e a o f 4 s l a n t △ s$ $"Surface Area of Pyramid = Area of rhombus base + Area of 4 slant triangles$

$A_{p} = A_{b} + 4 A_{s}$ $A_p = A_b + 4 A_s$

$b = 9, θ = \frac{5 π}{8}, h = 5$ $b = 9, theta = (5pi)/8, h = 5$

$A_{b} = b^{2} sin θ = 9^{2} sin (\frac{5 π}{8}) = 74.83$ $A_b = b^2 sin theta = 9^2 sin ((5pi)/8) = 74.83$

$4 \cdot A_{s} = 4 \cdot ((\frac{1}{2}) \cdot b \cdot l) = 2 \cdot 9 \cdot \sqrt{{(\frac{9}{2})}^{2} + 5^{2}}$ $4 * A_s = 4 * ((1/2) * b * l ) = 2 * 9 * sqrt((9/2)^2 + 5^2)$

$4 A_{s} = 121.08$ $4 A_s = 121.08$

$T S A of Pyramid A_{p} = 74.83 + 121.08 = 195.91$ $color(purple)(T S A " of Pyramid " A_p = 74.83 + 121.08 = 195.91$

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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 $5$ $5$ , its base's sides have lengths of $9$ $9$ , and its base has a corner with an angle of $\frac{5 π}{8}$ $(5 pi)/8$ . 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 55 , its base's sides have lengths of 99 , and its base has a corner with an angle of 5π8(5 pi)/8 . 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 $5$ $5$ , its base's sides have lengths of $9$ $9$ , and its base has a corner with an angle of $\frac{5 π}{8}$ $(5 pi)/8$ . What is the pyramid's surface area?