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.
LA = .5(15)(9.34)
LA = 70.05 sq. units