A triangular prism has base edges 4cm, 5cm, and 6cm long. Its lateral area is 300 cm2. What's the height if the prism?

Suppose you've got a triangle. Now, strech it up so as to make a stack of triangles up above another. This new 3d object is called a triangular prism.

Usually, when we talk about triangular prism, we talk about the triangular prism, whose stack goes straight up, thus, we talk about a right triangular prism.

For this case, it is specified that:

The base has edges of 4cm ,5cm and 6cm
The lateral surface area of the prism is 300 cm²
We've to find its height.

The triangular prism, as shown in the figure, has 3 rectangles.

Their one dimension is equal to the height of the prism.

Their second dimension is equal to the length of the corresponding side of the base and top triangle they're touching.

Thus, as the lateral surface area is the sum of areas of those 3 rectangles, thus:

300 = Sum of area of those 3 rectangles.

Let the heigth of the prism be h cm,

Then each rectangle has one side as of h cm, and other of either 4 cm, 5 cm, or of 6 cm.

Then, we get:

[tex]300 = h \times 4 + h \times 5 + h \times 6 \\300 = h(4 + 5 + 6)\\300 = 15h\\\text{Dividing both the sides by 15}\\\\h = \dfrac{300}{15} = 20 \: \rm cm[/tex]

Thus, the heigth of the considered triangular prism of the specified figures is obtained being of 20 cm.

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