Answer :

The area of a triangle is given by

[tex]A=\frac{b\cdot h}{2}[/tex]

where b is the base and h the height.

If the dimensions are tripled

[tex]\begin{gathered} b\longrightarrow3b \\ h\longrightarrow3h \end{gathered}[/tex]

then, the new area will be

[tex]\begin{gathered} A^{\prime}=\frac{3b\cdot3h}{2} \\ A^{\prime}=\frac{9b\cdot h}{2} \end{gathered}[/tex]

which is equal to

[tex]\begin{gathered} A^{\prime}=9(\frac{b\cdot h}{2}) \\ \sin ce\text{ the old area A is } \\ \\ A=\frac{b\cdot h}{2} \\ \text{the new are is} \\ A^{\prime}=9\cdot A \end{gathered}[/tex]

In other words, the new area A' will be 9 times the old area A. Since A is equal to 96 cm^2, we get

[tex]\begin{gathered} A^{\prime}=9\cdot96 \\ A^{\prime}=864 \end{gathered}[/tex]

that is, the new area will be 864 cm^2.