Find the surface area and volume

Mathematics
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Find the surface are and volume of a right prism with an isosceles trapezoid base. The bases of the trapezoid are 32 in and 20 in and the base angles of the trapezoid are 30 degrees. The height of the prism is 24 ins.

Apr 29th, 2015

the area of the trapezoid is given by 1/2(b1+b2)*h

1/2(32+20) = 1/2(52) = 26

tan 30 = h/6

h = 6tan30 = 3.464 in

Therefore the area of the trapezoid = 26(3.464) = 90 sq in.

The volume = area*height = (90)(24) = 2160 cubic inches

For the surface area we have to find the areas of all the faces:

(32)(24) = 768

(20)(24) = 480

the length of the angled face is found by

6/cos30 = 6.928

surface area of angled faces = 2(6.928)(24) = 332.55

plus the areas of the trapezoids = 2(90) = 180

Add them all up:

768+480+332.55+180 = 1760.55 square inches

Apr 29th, 2015

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Apr 29th, 2015
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