Problem

Which calculation gives the surface area of the rectangular pyramid?
\[
14 \times 4+2\left(\frac{1}{2} \times 2 \times \sqrt{245}\right)+2\left(\frac{1}{2} \times 7 \times \sqrt{200}\right)
\]
\[
14 \times 4+2\left(\frac{1}{2} \times 4 \times \sqrt{245}\right)+2\left(\frac{1}{2} \times 14 \times \sqrt{200}\right)
\]

Answer

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Answer

\(\boxed{\text{The correct calculation for the surface area of the rectangular pyramid is Expression 2 with a surface area of approximately 316.60 square units.}}\)

Steps

Step 1 :Calculate the surface area for both given expressions:

Step 2 :Expression 1: \(14 \times 4+2\left(\frac{1}{2} \times 2 \times \sqrt{245}\right)+2\left(\frac{1}{2} \times 7 \times \sqrt{200}\right)\)

Step 3 :Expression 2: \(14 \times 4+2\left(\frac{1}{2} \times 4 \times \sqrt{245}\right)+2\left(\frac{1}{2} \times 14 \times \sqrt{200}\right)\)

Step 4 :Surface area for Expression 1: \(186.30\) square units

Step 5 :Surface area for Expression 2: \(316.60\) square units

Step 6 :\(\boxed{\text{The correct calculation for the surface area of the rectangular pyramid is Expression 2 with a surface area of approximately 316.60 square units.}}\)

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