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.
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
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