# Trapezoidal prism

Calculate the surface of the quadrilateral prism ABCDA'B'C'D 'with the trapezoidal base ABCD. The height of the prism is 12 cm; ABCD trapezoidal data: AB base length is 8 cm, CD base length is 3 cm, BC arm length is 4 cm, and AC diagonal length is 7 cm.
Little help: Draw the trapezoid ABCD and measure its height and the arm AD.

Correct result:

S =  274.301 cm2

#### Solution:

$h=12 \ \text{cm} \ \\ a=8 \ \text{cm} \ \\ c=3 \ \text{cm} \ \\ b=4 \ \text{cm} \ \\ u=7 \ \text{cm} \ \\ h_{1}=3.499 \ \text{cm} \ \\ S_{1}=(a+c) \cdot \ h_{1} /2=(8+3) \cdot \ 3.499 /2=19.2445 \ \text{cm}^2 \ \\ d=4.651 \ \text{cm} \ \\ o=a+b+c+d=8+4+3+4.651=19.651 \ \text{cm} \ \\ S=o \cdot \ h + 2 \cdot \ S_{1}=19.651 \cdot \ 12 + 2 \cdot \ 19.2445=274.301 \ \text{cm}^2$

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