Surface area of a right triangular prism is the sum of lateral surface area and twice the base area of the triangular prism. Square units are used to measure the surface area of the prism.

### Formula for Surface Area of a Triangular Prism

We know,

Surface Area of a Prism = L + 2B

Where, L is lateral surface area and B is base area of the prism.

**In Triangular Prism, **

Lateral surface area (L) = Ph = (s_{1} + s_{2} + s_{3})h

Area of the base (B) = $\frac{1}{2}$ * a * b

Surface Area of Prism = (s_{1} + s_{2} + s_{3})h + 2($\frac{1}{2}$ab) = Ph + ab

Where, a = altitude, b = base, h = height and s_{1}, s_{2}, s_{3} are the sides of the triangular prism.

**Formula:**

Surface Area of Triangular Prism = Ph + ab = (s_{1} + s_{2} + s_{3})h + **ab**

Where, a = altitude, b = base, h = height and s_{1}, s_{2}, s_{3} are the sides.

Example:

Find the surface area of a triangular prism with the given altitude 3, base 4, height 5 and the sides 2, 3, 4.

**Solution:**

Given

Triangular prism with the altitude 3, base 4, height 5 and the sides 2, 3, 4.

Step 1:

Find the area of the base,

Area of the bases (B) = $\frac{1}{2}$ * a * b = $\frac{1}{2}$ * 3 * 4 = 6

=> Area of the base (B) = 6

Step 2:

Find the lateral surface area,

Lateral surface area (L) = Ph = (s_{1} + s_{2} + s_{3})h

= (2 + 3 + 4)5

= 9 * 5

= 45

=> Lateral surface area (L) = 45

Step 3:

Find the surface area of prism,

Surface Area of Prism = 2A + L = (2 * 6) + 45 = 12 + 45 = 57

Hence the area of the prism is 57 square units.