How To Find The Height Of A Triangular Prism

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Input the 3 triangle sides and the height:

A triangular prism is a geometric solid having 2 identical, parallel, triangular bases which are perpindicular to the iii rectangular faces.
In the in a higher place graphic, the light-green triangle is i of the bases and the ruby and blueish planes are two of the 3 faces.
The triangles can be whatever type of triangle (acute, correct or birdbrained).
This computer computes a triangular prism'southward area and volume when the triangle sides and prism height have been input.
It's great to have a estimator for computing triangular prisms, but let's see the mathematics of this.

A triangular prism has sides of v, half-dozen and 7 with a height of nine.
What is the surface area and volume of this prism?
The first matter to practise is to calculate the area of the triangular base of operations. Since nosotros know all three triangle sides, nosotros volition us Heron's Formula.

Semi-Perimeter = (5 + 6 + vii) ÷ 2
Semi-Perimeter = 18 ÷ 2
Semi-Perimeter = 9
Triangle Area = square root [9 * (9-v) * (9-6) * (9-7)]
Triangle Area = square root [9 * 4 * iii * ii]
Triangle Area = square root (216)
Triangle Area = xiv.6969384567

Since a triangular prism has ii triangles, the area of both triangles equals
2 * xiv.6969384567 = 29.3938769134

At present to summate the area of the iii rectangular faces:
Rectangular confront area = nine * (5 + 6 + vii)
Rectangular face area = 162
For the total prism expanse nosotros add up both areas:
Total Area = 29.3938769134 + 162
Total Area = 191.3938769134
Since we already calculated the triangle area, the volume is easily calculated by:
Book = triangle area * height
Volume = xiv.6969384567 * nine
Volume = 132.2724461103

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