To find the combined area of both bases of the prism, we first need to calculate the Lateral Surface Area (LSA) and then use the formula for Total Surface Area (TSA).

Calculating Lateral Surface Area (LSA)

The Lateral Surface Area of a prism is calculated by multiplying the perimeter of the base by the height of the prism.

• Base Perimeter ($P$) = 30 cm
• Height ($h$) = 7 cm
• The formula for LSA is:

  $LSA = P \times h$

• Substituting the values:

  $LSA = 30 \text{ cm} \times 7 \text{ cm} = 210 \text{ cm}^2$

Calculating Combined Base Area

The Total Surface Area (TSA) of a prism is the sum of the Lateral Surface Area (LSA) and the area of both bases (2 $\times$ Base Area).

• Total Surface Area ($TSA$) = 282 cm$^2$
• Lateral Surface Area ($LSA$) = 210 cm$^2$
• Let the area of both bases combined be $2B$.
• The formula for TSA is:

  $TSA = LSA + 2B$

• We need to find $2B$. Rearranging the formula:

  $2B = TSA - LSA$

• Substituting the values:

  $2B = 282 \text{ cm}^2 - 210 \text{ cm}^2$

• Therefore, the combined area of both bases is:

  $2B = 72 \text{ cm}^2$

The area of both bases combined is 72 cm$^2$.