Question

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

Answer 1

Answer:

$\large\boxed{V=\dfrac{75\sqrt3}{2}\approx64.95}\\\boxed{S.A.=\dfrac{160+25\sqrt3}{2}}$

Step-by-step 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:

$A=\dfrac{a^2\sqrt3}{4}$

Substitute a = 5:

$B=\dfrac{5^2\sqrt3}{4}=\dfrac{25\sqrt3}{4}$

H = 6.

Calculate the volume:

$V=\left(\dfrac{25\sqrt3}{4}\right)(6)=\dfrac{75\sqrt3}{2}$

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:

$S.A.=2\left(\dfrac{25\sqrt3}{4}\right)+(15)(6)=\dfrac{25\sqrt3}{2}+80=\dfrac{160+25\sqrt3}{2}$