# Formula For Surface Area Of A Triangular Prism

## Formula For Surface Area Of A Right Triangular Prism

To find the Surface Area of a right triangular prism, the formula is

$A = ah + bh + ch + ab$

where a, b and c are the sides of the triangle and h is the length of the prism. {c is the hypotenuse of the triangle}

The two right triangular sides have the total surface area of 2 (1/2) ab = ab. The sides are each: ah, bh and ch

## Formula For Surface Area Of Any General Triangular Prism

The formula for surface area of any general triangular prism, is

$A = 2\sqrt{s(s-a)(s-b)(s-c)} + ah + bh + ch$

where $s = \frac{a + b + c}{2}$

The area of one triangular sides is as per Hero’s Formula.
$= \sqrt{s(s-a)(s-b)(s-c)}$
The sides are each: ah, bh and ch

Example-1:
Right Triangular Prism of Length 10 cm

Sides are {a = 5; b = 12; c =13}

Surface Area (A) = (5)(10) + (12)(10) + (13)(10)
= 50 + 120 + 130 = 300 cm²

Example-2:
Any General Triangular Prism of Length 10 cm
Sides are {a = 6; b = 8; c = 10}

As per Hero’s Formula,
s = (a + b + c)/2 = (6 + 8 + 10)/2 = 12

So, the Area of one of the triangular face
= $\sqrt{12*6*4*2} = \sqrt{576} = 24$

So, Surface Area (A) = 2(24) + (6)(10) + (8)(10) + (10)(10)
= 48 + 60 + 80 + 100 = 50 + 120 + 130 = 288 cm²