Question

Please help me find the surface area of this right prism. ASAP please. Thank you ~

Answer 1

`\large\boxed{V=(75\sqrt3)/(2)\approx64.95}\\\boxed{S.A.=(160+25\sqrt3)/(2)}`

Explanation:

The formula of a volume of a prism:

`V=BH`

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:

`A=(a^2\sqrt3)/(4)`

Substitute a = 5:

`B=(5^2\sqrt3)/(4)=(25\sqrt3)/(4)`

H = 6.

Calculate the volume:

`V=\left((25\sqrt3)/(4)\right)(6)=(75\sqrt3)/(2)`

The formula of a Surface Area:

`S.A.=2B+PH`

B - base area

P - perimeter of a base

H - height

Calculate P:
`P=5+5+5=15`

Substitute:

`S.A.=2\left((25\sqrt3)/(4)\right)+(15)(6)=(25\sqrt3)/(2)+80=(160+25\sqrt3)/(2)`