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Find the surface area of the figure in square millimeters.

Find the surface area of the figure in square millimeters.-example-1
User Igrinis
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1 Answer

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Find the area of the shapes that limit the figure, it means, find the area of the 2 triangles and the 3 rectangles that compose the figure.

Rectangles:


\begin{gathered} A=b\cdot h \\ A=7\operatorname{mm}\cdot24\operatorname{mm} \\ A=168\operatorname{mm} \end{gathered}

Triangles (but first it is necessary to find the height of the triangles using the pythagorean theorem)


\begin{gathered} h=\sqrt[]{24^2-12^2} \\ h=\sqrt[]{576-144} \\ h=\sqrt[]{432} \\ h=20.78 \end{gathered}
\begin{gathered} A=(b\cdot h)/(2) \\ A=\frac{24\operatorname{mm}\cdot20.78\operatorname{mm}}{2} \\ A=249.36\operatorname{mm} \end{gathered}

The last step is to add 3 times the area of the rectangle plus 2 times the area of the triangle to find the total surface area.


\begin{gathered} AT=3\cdot168\operatorname{mm}+2\cdot249.36\operatorname{mm} \\ AT=1,002.72\operatorname{mm} \end{gathered}

The surface area of the figure is 1002.72mm^2. The right answer is the third one.

User Jakub Vano
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