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5 mm 40 mm 8 mm 5 mm mm 8 mm What is the surface area of the prism represented by the net? 53 mm 106 mm 560 mm 1.120 mm 5 mm 8 mm 40 mm M

User Alvivi
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1 Answer

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To determine the surface area of the prism, you have to determine the area of each rectangular face of the prism and then add all areas.

The prism has 3 sets of equal faces:

Two are 40mm x 8mm rectangles

Two are 40mmx5mm rectangles

Two are 8mmx5mm rectangles

The area of any rectangle can be calculated as the product of its length and width, so that:


A=lw

1) Area of 40x8 rectangles:


\begin{gathered} A_1=40\cdot8=320\operatorname{mm} \\ 2A_1=640\operatorname{mm}^2 \end{gathered}

2) Area of the 40x5 rectangles


\begin{gathered} A_2=40\cdot5=200\operatorname{mm}^2 \\ 2A_2=2\cdot200=400\operatorname{mm}^2 \end{gathered}

3) Area of the 8x5 rectangles:


\begin{gathered} A_3=8\cdot5=40\operatorname{mm}^2 \\ 2A_3=2\cdot40=80\operatorname{mm}^2 \end{gathered}

Now you can determine the surface area of the rectangular prism:


\begin{gathered} SA=2A_1+2A_2+2A_3 \\ SA=640+400+80 \\ SA=1120\operatorname{mm}^2 \end{gathered}

The surface area of the prism is 1120mm²

User Niya
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