Question

How can I get the total area of this shape?

Answer 1

The total area (surface area) of this triangular prism is given by the area of the two smaller triangles in the base, the two lateral rectangles and the rectangular base.

First, we will need to calculate the third side of the triangle in the base, using the Pythagorean theorem:

`\begin{gathered} BD^2=BC^2+CD^2 \\ BD^2=8^2+6^2 \\ BD^2=64+36 \\ BD^2=100 \\ BD=10 \end{gathered}`

Now, calculating each area and adding them, we have:

`\begin{gathered} S=2\cdot((6\cdot8)/(2))+12\cdot10+12\cdot8+12\cdot6 \\ S=48+120+96+72 \\ S=336 \end{gathered}`

Therefore the total area is 336 cm².