Find the lateral area of an equilateral triangle base right prism with base edge 5 and height 9

We are asked to find the lateral area of a right prism
which has an equilateral triangle as a base.  The base edge is 5, and the height of the
prism is 9.

We will use the formula lateral area =
1/2(perimeter)(slant height)

=> A =
1/2pl

First, we will need to find (l) which is the slant
height of the prism.  To do so, we need to apply the
following:

=> The given height is perpendicular to
the base.  This creates a right triangle.  We can use the Pythagorean Theorem to solve
for slant height of the triangle.

=> The slant
height is the hypotenuse of the triangle.

=>
One-half of the edge of the triangular base will be a leg of the right triangle. 
Therefore, 2.5 is one leg of the triangle.

=> We
will use the given height as the other leg.

We substitute
these values into the Pythagorean Theorem and solve for the
hypotenuse.

c^2 = a^2 +
b^2

c^2 = 9^2  + 2.5^2

c^2 =
87.25

c = 9.34

We now use the
formula for lateral area.

LA =
1/2pl

(p) is the perimeter of the triangular base = 3(5) or
15.

(l)= 9.34

LA =
.5(15)(9.34)

LA =  70.05 sq.
units