Calculate 258

Calculate the volume and surface area of a prism with a trapezoidal base and a height of 9 cm. The base is an isosceles trapezoid with parallel sides of 3 cm and 6 cm, legs of 2.5 cm, and a height of 2 cm.

Final Answer:

V =  81 cm³
S =  144 cm²

Step-by-step explanation:

$$\begin{gathered} h=9\text{cm} \\ c=3\text{cm} \\ a=6\text{cm} \\ r=2.5\text{cm} \\ {h}_2=2\text{cm} \\ {S}_1=\frac{a+c}{2}\cdot h_2=\frac{6+3}{2}\cdot 2=9{\text{cm}}^2 \\ V=S_1\cdot h=9\cdot 9=81{\text{cm}}^3 \end{gathered}$$

$$\begin{gathered} S_2=(a+c+2\cdot r)\cdot h=(6+3+2\cdot 2.5)\cdot 9=126{\text{cm}}^2 \\ S=2\cdot S_1+S_2=2\cdot 9+126=144{\text{cm}}^2 \end{gathered}$$

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