Jewelry box

The jewelry box is in the shape of a four-sided prism with the base of an isosceles trapezoid with sides a=15 centimeters, b is equal to 9 centimeters, c is equal to 10 centimeters, c is equal to 7 whole 4 centimeters. How much fabric is needed to cover a jewelry box if its height is 7 centimeters?

Final Answer:

S =  474.8071 cm²

Step-by-step explanation:

$$\begin{gathered} a=15\text{cm} \\ b=9\text{cm} \\ c=10\text{cm} \\ v=7.4\text{cm} \\ h=7\text{cm} \\ {S}_1=(a+c)\cdot v/2=(15+10)\cdot 7.4/2=\frac{185}{2}=92.5{\text{cm}}^2 \\ {a}_1=\sqrt{b^2-v^2}=\sqrt{9^2-7.4^2}\doteq 5.1225\text{cm} \\ {a}_2=a-(c+a_1)=15-(10+5.1225)\doteq -0.1225\text{cm} \\ d=\sqrt{a_2^2+v^2}=\sqrt{(-0.1225{)}^2+7.4^2}\doteq 7.401\text{cm} \\ o=a+b+c+d=15+9+10+7.401\doteq 41.401\text{cm} \\ S=2\cdot S_1+o\cdot h=2\cdot 92.5+41.401\cdot 7=474.8071{\text{cm}}^2 \end{gathered}$$

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