A rhombic prism has the diagonal of the rhombus measuring 16 and 12 cm. If the the altitude of the prism is equal in size to the side of the rhombus. What is the surface area and the volume of the Rhombic Prism?

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A rhombic prism has the diagonal of the rhombus measuring 16 and 12 cm. If the the altitude of the prism is equal in size to the side of the rhombus. What is the surface area and the volume of the Rhombic Prism?

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Answer 1 · 2018-01-11T14:06:12

Total Surface Area of Rhombuic Prism $T S A = 592 c m^{2}$ $T S A = color(red)(592 cm^2)$

Volume of Rhobic Prism $V_{R} = 960 c m^{3}$ $V_R = color (blue)(960 cm^3)$

Explanation:

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Area of Rhombus base $A_{R} = (\frac{1}{2}) \cdot D 1 \cdot D 2 = (\frac{1}{2}) \cdot 16 \cdot 12 = 96 c m^{2}$ $A_R = (1/2) * D1 * D2 = (1/2) * 16 * 12 = 96 cm^2$

Side of Rhombus $a = \sqrt{{(\frac{D 1}{2})}^{2} + {(\frac{D 2}{2})}^{2}}$ $a = sqrt(((D1)/2)^2 + ((D2)/2)^2)$

$a = \sqrt{8^{2} + 6^{2}} = 10 c m$ $a = sqrt(8^2 + 6^2) = 10 cm$

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Height of prism $h = a = 10 c m$ $h = a = 10 cm$

Lateral Surface Area $A_{L} = 4 \cdot (10 \cdot 10) = 400 c m^{2}$ $A_L = 4 * (10*10) = 400 cm^2$

Total Surface Area $T S A = L S A + 2 A_{R} = 400 + (2 \cdot 96) = 592 c m^{2}$ $T S A = L S A + 2 A_R = 400 + (2*96) = color(red)(592 cm^2)$

Volume of Rhombus $V_{R} = A_{R} \cdot h = 96 \cdot 10 = 960 c m^{3}$ $V_R = A_R * h = 96 * 10 = color(blue)(960 cm^3)$

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A rhombic prism has the diagonal of the rhombus measuring 16 and 12 cm. If the the altitude of the prism is equal in size to the side of the rhombus. What is the surface area and the volume of the Rhombic Prism?

1 Answer

Explanation:

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