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, the height of trapezium v = 3.7 cm, and the height of the prism h = 5 cm.

Final Answer:

S =  144.4 cm²
V =  111 cm³

Step-by-step explanation:

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

$V=S_1\cdot h=\frac{111}{5}\cdot 5=\frac{111\cdot 5}{5}=\frac{555}{5}=111{\text{cm}}^3$

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