Base RR odd

The base of a prism is an isosceles trapezoid ABCD with bases AB = 12 cm and CD = 9 cm. The angle at vertex B is 48°10′.

Determine the volume and surface area of the prism if its height is 35 cm.

Final Answer:

S =  927.6189 cm²
V =  615.8182 cm³

Step-by-step explanation:

$$\begin{gathered} a=12\text{cm} \\ c=9\text{cm} \\ \beta =48°10^{\prime }=48°+\frac{10}{60}°=48.1667°\doteq 48.1667 \\ {h}_2=35\text{cm} \\ x=\frac{a-c}{2}=\frac{12-9}{2}=\frac{3}{2}=1.5\text{cm} \\ \tan \beta =h:x \\ h=x\cdot \tan \beta =x\cdot \tan 48.166666666667°=1.5\cdot \tan 48.166666666667°=1.5\cdot 1.11713=1.6757\text{cm} \\ b=\sqrt{h^2+x^2}=\sqrt{1.6757^2+1.5^2}\doteq 2.249\text{cm} \\ {S}_1=\frac{a+c}{2}\cdot h=\frac{12+9}{2}\cdot 1.6757\doteq 17.5948{\text{cm}}^2 \\ o=a+c+2\cdot b=12+9+2\cdot 2.249\doteq 25.498\text{cm} \\ {S}_2=o\cdot h_2=25.498\cdot 35\doteq 892.4293\text{cm} \\ S=2\cdot S_1+S_2=2\cdot 17.5948+892.4293=927.6189{\text{cm}}^2 \end{gathered}$$

$V=S_1\cdot h_2=17.5948\cdot 35=615.8182{\text{cm}}^3$

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