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 = color(red)(592 cm^2)#

Volume of Rhobic Prism #V_R = color (blue)(960 cm^3)#

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Area of Rhombus base #A_R = (1/2) * D1 * D2 = (1/2) * 16 * 12 = 96 cm^2#

Side of Rhombus #a = sqrt(((D1)/2)^2 + ((D2)/2)^2)#

#a = sqrt(8^2 + 6^2) = 10 cm#

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Height of prism #h = a = 10 cm#

Lateral Surface Area #A_L = 4 * (10*10) = 400 cm^2#

Total Surface Area #T S A = L S A + 2 A_R = 400 + (2*96) = color(red)(592 cm^2)#

Volume of Rhombus #V_R = A_R * h = 96 * 10 = color(blue)(960 cm^3)#