Vertical prism

The base of the vertical prism is a rhombus with diagonals of 24 cm and 10 cm. Suppose the shell area is 52% of the total surface area of the prism. Calculate its surface.

Final Answer:

S =  250 cm²

Step-by-step explanation:

$$\begin{gathered} u=24\text{cm} \\ v=10\text{cm} \\ {S}_1=u\cdot v/2=24\cdot 10/2=120{\text{cm}}^2 \\ S=S_1+S_2 \\ {S}_2=0.52\cdot S \\ (S-S_1)=0.52\cdot S \\ (S-120)=0.52\cdot S \\ 0.48S=120 \\ S=\frac{120}{0.48}=250 \\ S=250=250{\text{cm}}^2 \end{gathered}$$

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