SOLUTION: find the surface area of isosceles trapezoid prism with given B1=8 cm B2 =14 cm height =4cm and length =10cm.

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Question 1159981: find the surface area of isosceles trapezoid prism with given B1=8 cm B2 =14 cm height =4cm and length =10cm.
Answer by MathLover1(20850) About Me  (Show Source):
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find the surface area of isosceles trapezoid prism with given
b%5B1%5D=8cm+
b%5B2%5D+=14cm+
heighth+=4cm and
length l=10cm

The surface area
S=2%2AA%5Bbase%5D+Lateral Surface Area

A%5Bbase%5D=%28h%2F2%29%28b%5B1%5D%2Bb%5B2%5D%29
L=Lateral Surface Area= the sum of the areas of each surface around the base.

L=b%5B1%5Dl%2Bcl%2Bb%5B2%5Dl%2Bdl

Substitute each piece into the equation:
S=2%2A%28h%2F2%29%28b%5B1%5D%2Bb%5B2%5D%29%2Bb%5B1%5Dl%2Bcl%2Bb%5B2%5Dl%2Bdl
Simplify:
S=h%28b%5B1%5D%2Bb%5B2%5D%29%2Bb%5B1%5Dl%2Bcl%2Bb%5B2%5Dl%2Bdl
Distribute and Rearrange:
S=hb%5B1%5D%2Bhb%5B2%5D%2Bb%5B1%5Dl%2Bcl%2Bb%5B2%5Dl%2Bdl
S=b%5B1%5D%28h%2Bl%29%2Bb%5B2%5D%28h%2Bl%29%2Bcl%2Bdl
given that trapezoid is isosceles ,so the legs are congruent by definition and
c=d
S=b%5B1%5D%28h%2Bl%29%2Bb%5B2%5D%28h%2Bl%29%2Bcl%2Bcl
S=b%5B1%5D%28h%2Bl%29%2Bb%5B2%5D%28h%2Bl%29%2B2cl
to find c use right triangle with one leg h=4, other leg half of difference between bases, and hypotenuse is c
leg half of difference between bases:%2814-8%29%2F2=6%2F2=3
=>c%5E2=3%5E2%2B4%5E2
c=sqrt%289%2B16%29
c=sqrt%2825%29
c=5
and, surface area is:
S=8%284%2B10%29%2B14%284%2B10%29%2B2%2A5%2A10
S=408cm%5E2