The base of a triangular prism is an equilateral triangle...

The base of a triangular prism is an equilateral triangle with a perimeter of 24 inches. If the height of the prism is 5 inches, find the lateral area.
(E) 120 in $^{2}$
(G) 60 in $^{2}$
(H) 40 in $^{2}$
( J)360 in $^{2}$
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Key Concepts

Equilateral Triangle

An equilateral triangle is a type of triangle where all three sides and all three angles are equal. Its property of equal sides allows for straightforward calculation of its perimeter by multiplying the length of one side by three, a step often used in geometric problems involving regular shapes.

Perimeter of a Polygon

The perimeter of a polygon is the sum of the lengths of all its sides. This concept is crucial when dealing with regular polygons, where the calculation simplifies to multiplying the length of one side by the total number of sides, providing a key component in formulas like that for lateral area.

Triangular Prism

A triangular prism is a three-dimensional solid with two parallel, congruent triangular bases and three rectangular lateral faces connecting the corresponding sides of the bases. Understanding its structure is essential for calculating various properties, such as lateral area and volume, using its dimensions.

Lateral Area

The lateral area of a prism is the total area of all its lateral (side) faces. For prisms, it is calculated by multiplying the perimeter of the base by the height of the prism, which reflects how these rectangular faces extend along each side of the base over the given height.

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