Triangular prisms are three sided prism. The flat surface is called faces of the triangular prism. It has six vertices. Formula to find the surface area and volume of the prism is given below.

**Surface area and volume of right triangular prism:**

**Total surface area T.S.A = (P x h + 2 A) sq. units **

** P = perimeter of base (a + b + c)**

** h = height of the prism**

** A = Area of the base**

**Volume of the prism (V) = ½ Al cubic units**

Rectangular prisms are one type of the prism. It has four sides. It has eight vertices. Formula to find the surface area and volume of the prism is given below.

** Surface area and volume of rectangular prism:**

** **

** Total surface area of rectangular prism**

**
= 2 (length x breadth + breadth x width + length x height)**

**
=2(lb + bh+ lh) square units**

** Volume of the rectangular prism (V) = l x w h cubic units**

1. The base of a prism is a right angled triangle of side 4 cm, 3cm and 5 cm. its length is 10 cm. find total surface area and volume of prism.

**Solution:**

**Given:**

Let us take the base of the right triangular prism = 4 cm

Height (h) =3 cm

Length of the prism = 10 cm

**Formula:**

**Total surface area T.S.A = (P x l + 2 A) sq. units**

** Perimeter (p) = a + b + c**

= 4 + 3 + 5

= 12 cm

** Area of the base (A) = ½ (base x height)**

= ½ (4 x 3)

= 12/2

= 6 cm^{2}

Substitute in the formula,

** T.S.A = (12 x 10 + 2 x 6)**

= 120 + 12

=
132 cm^{3}

**Total surface area T.S.A = 132 cm ^{2}**

** **

**Volume of the prism (V) = ½ Al cubic units**

** **
= ½ (6 x 10)

=60 / 2

** Volume of the prism = 30 cubic units**

1. Find the lateral surface area and total surface area of a rectangular whose length is 10 cm, width 8cm and height 6cm.

**Solution:**

**Given:**

Length (l) = 10cm

Width (w) = 8 cm

Height (h) = 6 cm

**Total surface area of rectangular prism =2(wh + lw+ lh) square units**

= 2(8 x 6+ 10 x 8 + 10 x 6)

= 2 (48 + 80 + 60)

= 2 (188)

= 376

**Total surface area of rectangular prism = 376 cm ^{2}**

** Volume of the rectangular prism (V) = l x w x h cubic units**

** **
= 10 x 8 x 6

= 80 x 6

**
= 480 cm ^{3}**