Question

What is the T.A. = and V =

Answer 1

The formula of the area of the equilateral triangle:
$A_\Delta=\dfrac{a^2\sqrt3}{4}\\\\a=3\to A_\Delta=\dfrac{3^2\sqrt3}{4}=\dfrac{9\sqrt3}{4}$

The formula of the area of the rectangle:
$A=width\times length=wl\\\\w=3;\ l=6\\\\A=3\cdot6=18$

$T.A.=2A_\Delta+3A\\\\T.A.=2\cdot\dfrac{9\sqrt3}{4}+3\cdot18=\dfrac{9\sqrt3}{2}+54=(54+4.5\sqrt3)\ in^2$
The formula of the volume of the triangular prism:
$V=A_\Delta\cdot l\\\\V=\dfrac{9\sqrt3}{4}\cdot6=\dfrac{9\sqrt3}{2}\cdot3=\dfrac{27\sqrt3}{2}=13.5\sqrt3\ in^3$