## Note on Triangular Prism

• Note
• Things to remember
• Exercise

A triangular prism is a prism whose bases are triangles and whose lateral faces are rectangles. It has 9 edges and 6 vertices.

#### Total Surface Area and Volume of Triangular Prism

The volume of a triangular prism can be found by multiplying the base times the height.

Because the triangle is right triangle,

a2 = 32 + 42

a= 9+16

a2 = 25

a = 5

So, the prism is:

The prism has two faces in dimension:

Area of each face = $$\frac{1}{2}$$ x 3 x 4 = 6

Area of both faces = 6 + 6 = 12

It has one face of dimension:

Area = 5 x 6 = 30

It has one face of dimension

Area = 4 x 6 = 24

It has one face of dimension:

Area = 3 x 6 = 18

Total surface area of the sum of these:

Total surface area = 12+30+24=18 = 84

Now, lateral surface area = area of 3 rectangles

= 5 x 6 + 4 x 6 + 3 x 6

= (5 + 4 +3) x 6

= perimeter of triangular base x height of prism.

Thus, total surface area = lateral surface area + 2 x area of the triangular base

Also, volume of the triangular prism = area of base x height

Example:

Find the volume of the given triangular prism.

Solution:
Area of base (A) = area of ΔABC

= $$\frac{1}{2}$$ x 4cm x 2cm

= 4cm2

Height of the prism (h) = 15 cm

Volume of prism (V) = A x h

= 4 x 15

= 60cm3

• A triangular prism is a prism whose bases are triangles and whose lateral faces are rectangles. It has 9 edges and 6 vertices.
• Lateral Surface Area = Area of rectangles
• Total Surface Area = Lateral Surface Area + 2 x Area of the triangular base
.

### Very Short Questions

Triangular prism

Solution:

Area of base (A) = area of $$\triangle$$ABC

= $$\frac{1}{2}$$ $$\times$$ 6cm $$\times$$ 8cm

= 24cm2

Height of prism (h) = 12cm

Volume of prism (V) = A $$\times$$ h

= 24cm2 $$\times$$12cm

= 288cm3

Solution:

Area of base (A) = area of $$\triangle$$ABC

= $$\frac{1}{2}$$ $$\times$$ 24cm $$\times$$ 7cm

= 84cm2

Height of prism (h) = 30cm

Volume of prism (V) = A $$\times$$ h

= 84cm2 $$\times$$ 30cm

= 2520cm3

Solution:

Area of base (A) = area of $$\triangle$$ABC

= $$\frac{1}{2}$$ $$\times$$ 14cm $$\times$$ 8cm

= 56cm2

Height of prism (h) = 25cm

Volume of prism (V) = A $$\times$$ h

= 56cm2 $$\times$$ 25cm

= 1400cm3

Solution:

Area of base (A) = area of triangle

= $$\frac{1}{2}$$$$\times$$12cm$$\times$$9cm

= 54cm2

Height of prism (h) = 18cm

Volume of prism(V) = A$$\times$$h

= 54cm2$$\times$$18cm

= 972cm3

Solution:

Area of base (A) = area of triangle

= $$\frac{1}{2}$$$$\times$$4cm$$\times$$6cm

= 12cm2

Height of prism (h) = 8cm

Volume of prism (V) = A$$\times$$h

= 12cm2$$\times$$8cm

= 96cm3

Solution:

Area of base (A) = area of triangle

= $$\frac{1}{2}$$$$\times$$4.5cm$$\times$$5cm

= 11.25cm2

Height of prism (h) = 8cm

Volume of prism(V) = A$$\times$$h

= 11.25cm2$$\times$$8cm

= 90cm3

Solution:

Area of base(A) = area of $$\triangle$$ABD

= $$\frac{1}{2}$$$$\times$$4cm$$\times$$3cm

= 6cm2

Height of prism = h

Volume of prism (V) = A$$\times$$h

42cm3 = 6cm2$$\times$$h

h = $$\frac{42cm^3}{6cm^2}$$

h = 7cm

Solution:

Lateral surface area = area of 3 rectangles

= 3.5$$\times$$8+4.5$$\times$$8+6$$\times$$8

= 112cm2

Solution:

Because the triangle is right angled triangle

a2 = 82 + 62

a2 = 64 + 36

a2 = 100

a = 10

Lateral surface area = area of 3 rectangles

= 10$$\times$$30+8$$\times$$30+6$$\times$$30

= 720cm2

Solution:

Because the triangle is right angled triangle

a2 = 42 +32

a2 = 16 +9

a2 =25

a =5

Lateral surface area = area of 3 rectangles

= 5$$\times$$10 + 4$$\times$$10 + 3$$\times$$10

= 120cm2

Solution:

Because the triangle is right angled triangle

AC2 = AB2 + BC2

AC2 = 52 +122

AC2 = 25 +144

AC2 =169

AC =13

Area of each face = $$\frac{1}{2}$$$$\times$$5$$\times$$12

= 30cm2

Area of both face = 30cm2 + 30cm

= 60cm2

Total surface area = area of both face + area of 3 rectangles

= 60cm2+ 5$$\times$$30 + 12$$\times$$30 + 13$$\times$$30

= 960cm2

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