Answer:
[tex]\large\boxed{V=\dfrac{75\sqrt3}{2}\approx64.95}\\\boxed{S.A.=\dfrac{160+25\sqrt3}{2}}[/tex]
Step-by-step explanation:
The formula of a volume of a prism:
[tex]V=BH[/tex]
B - base area
H - height
In the base we have the equilateral triangle. The formula of an area of an equilateral triangle with side a:
[tex]A=\dfrac{a^2\sqrt3}{4}[/tex]
Substitute a = 5:
[tex]B=\dfrac{5^2\sqrt3}{4}=\dfrac{25\sqrt3}{4}[/tex]
H = 6.
Calculate the volume:
[tex]V=\left(\dfrac{25\sqrt3}{4}\right)(6)=\dfrac{75\sqrt3}{2}[/tex]
The formula of a Surface Area:
[tex]S.A.=2B+PH[/tex]
B - base area
P - perimeter of a base
H - height
Calculate P: [tex]P=5+5+5=15[/tex]
Substitute:
[tex]S.A.=2\left(\dfrac{25\sqrt3}{4}\right)+(15)(6)=\dfrac{25\sqrt3}{2}+80=\dfrac{160+25\sqrt3}{2}[/tex]
