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; Trapezoid ABCD has the following dimensions: 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.

Final Answer:

S =  274.301 cm²

Step-by-step explanation:

$$\begin{gathered} h=12\text{cm} \\ a=8\text{cm} \\ c=3\text{cm} \\ b=4\text{cm} \\ u=7\text{cm} \\ {h}_1=3.499\text{cm} \\ {S}_1=(a+c)\cdot h_1/2=(8+3)\cdot 3.499/2=19.2445{\text{cm}}^2 \\ d=4.651\text{cm} \\ o=a+b+c+d=8+4+3+4.651=19.651\text{cm} \\ S=o\cdot h+2\cdot S_1=19.651\cdot 12+2\cdot 19.2445=274.301{\text{cm}}^2 \end{gathered}$$

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