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Note on Triangular Prism

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

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Total Surface Area and Volume of Triangular Prism

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

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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

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It has one face of dimension:

Area = 5 x 6 = 30

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It has one face of dimension

Area = 4 x 6 = 24

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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.

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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
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Very Short Questions

Solution:

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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:

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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:

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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:

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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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