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 has sides of length $4$ $4$ , and its base has a corner with an angle of $\frac{3 π}{8}$ $(3 pi)/8$ . 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 has sides of length $4$ $4$ , and its base has a corner with an angle of $\frac{3 π}{8}$ $(3 pi)/8$ . What is the pyramid's surface area?

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Answer 1 · 2018-02-23T13:36:33

Total Surface Area $T S A = A_{b} + L_{s} = 14.78 + 43.12 = 57.9$ $T S A = A_b + L_s = 14.78 + 43.12 = 57.9$ sq units

Explanation:

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Base area of the pyramid $A_{b} = l^{2} sin θ$ $A_b = l^2 sin theta$

$A_{b} = 4^{2} sin (\frac{3 π}{8}) = 14.78$ $A_b = 4^2 sin ((3pi)/8) = 14.78$

Slant height of the pyramid $s = \sqrt{{(\frac{l}{2})}^{2} + h^{2}}$ $s = sqrt((l/2)^2 + h^2)$

$s = \sqrt{{(\frac{4}{2})}^{2} + 5^{2}} = 5.39$ $s = sqrt((4/2)^2 + 5^2) = 5.39$

Lateral Surface Area of pyramid ( $L_{s}$ $L_s$ ) = 4 * Area of slant triangle ( $4 \cdot A_{s}$ $4 * A_s$ )

$L_{s} = 4 \cdot A_{s} = 4 \cdot (\frac{1}{2}) \cdot l \cdot s = 4 \cdot (\frac{1}{2}) \cdot 4 \cdot 5.39 = 43.12$ $L_s = 4 * A_s = 4 * (1/2) * l * s = 4 * (1/2) * 4 * 5.39 = 43.12$

Total Surface Area $T S A = A_{b} + L_{s} = 14.78 + 43.12 = 57.9$ $T S A = A_b + L_s = 14.78 + 43.12 = 57.9$ 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 $5$ $5$ , its base has sides of length $4$ $4$ , and its base has a corner with an angle of $\frac{3 π}{8}$ $(3 pi)/8$ . 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 has sides of length 44 , and its base has a corner with an angle of 3π8(3 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 has sides of length $4$ $4$ , and its base has a corner with an angle of $\frac{3 π}{8}$ $(3 pi)/8$ . What is the pyramid's surface area?