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