What is the most simple surface area formula for a triangular prism?

Answer 1

It depends on the exact shape and what information you have.

The simplest formula will apply if it is a right angled triangle. Suppose the base of the triangle is B cm and its height is H cm. Also suppose the length of the prism is L cm.

By Pythagoras, the third side of the triangle is the hypotenuse with length = C = sqrt(B2 + H2) cm.

Now the area of each triangular face is 0.5*B*H so the area of the two triangular faces is B*H cm2.

Also, the three rectangular faces have areas of B*L, H*L and C*L cm2 = L*(B+H+C) cm2.

Add the areas of the triangles and rectangles together.

If the triangle is equilateral, and each of its sides is of length S cm, then each triangular face has an area of S*sqrt(3)/4 cm2 so that the two faces sum to S*sqrt(3)/2 cm2. Each of the three rectangular faces has an area of L*S cm2 so together the rectangular faces sum to 3*L*S cm2.

If the triangle is neither right angled nor equilateral, but you have all three sides, the formula is a bit more complicated.

If the sides are A, B and C cm then calculate T = (A+B+C)/T. Area of triangle = 0.5*sqrt[(T*(T-A)*(T-B)*(T-C)] cm2 and the rectangles sum to L*(A+B+C) cm2.

If you have two sides of the triangle and the included angle, you will need to calculate the third side before you can proceed as above.

If you have one side and two angle (and therefore all three), you will need to calculate the missing sides before you can proceed as above.

For other specifications of the triangular faces, the formulae become seriously difficult.