Trapezoidal base

Calculate the surface and volume of a quadrilateral prism with a trapezoidal base, where a = 7 cm, b = 4 cm, c = 5 cm, d = 4 cm, height of trapezium v = 3.7 cm and the height of the prism h = 5 cm.

Correct answer:

S =  144.4 cm²
V =  111 cm³

Step-by-step explanation:

$$\begin{gathered} a=7\text{ cm } \\ b=4\text{ cm } \\ c=5\text{ cm } \\ d=4\text{ cm } \\ v=3.7\text{ cm } \\ h=5\text{ cm } \\ {S}_1={\displaystyle \frac{a+c}{2}}\cdot v={\displaystyle \frac{7+5}{2}}\cdot 3.7={\displaystyle \frac{111}{5}}=22.2{\text{cm}}^2 \\ o=a+b+c+d=7+4+5+4=20\text{ cm } \\ {S}_2=o\cdot h=20\cdot 5=100{\text{cm}}^2 \\ S=2\cdot S_1+S_2=2\cdot 22.2+100={\displaystyle \frac{722}{5}}={\displaystyle \frac{722}{5}}{\text{cm}}^2=144.4{\text{cm}}^2 \end{gathered}$$

$V=S_1\cdot h=22.2\cdot 5=111{\text{cm}}^3$

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