Rhombus base

Calculate the volume and surface area of prisms whose base is a rhombus with diagonals u1 = 12 cm and u2 = 15 cm. Prism height is twice base edge length.

Correct result:

V =  1728.84 cm3
S =  918 cm2

Solution:

u1=12 cm u2=15 cm  (u1/2)2+(u2/2)2=a2  a=(u1/2)2+(u2/2)2=(12/2)2+(15/2)29.6047 cm  S1=u1 u22=12 152=90 cm2  h=2 a=2 9.6047=3 41 cm19.2094 cm  V=S1 h=90 19.2094=270 41=1728.84 cm3
o=4 a=4 9.6047=6 41 cm38.4187 cm  S2=o h=38.4187 19.2094=738 cm2  S=2 S1+S2=2 90+738=918 cm2



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