A triangular prism is a prism whose bases are triangles and whose lateral faces are rectangles. It has 9 edges and 6 vertices.
The volume of a triangular prism can be found by multiplying the base times the height.
Because the triangle is right triangle,
a^{2} = 3^{2} + 4^{2}
a^{2 }= 9+16
a^{2} = 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
= 4cm^{2}
Height of the prism (h) = 15 cm
Volume of prism (V) = A x h
= 4 x 15
= 60cm^{3}
Triangular prism
Solution:
Area of base (A) = area of \(\triangle\)ABC
= \(\frac{1}{2}\) \(\times\) 6cm \(\times\) 8cm
= 24cm^{2}
Height of prism (h) = 12cm
Volume of prism (V) = A \(\times\) h
= 24cm^{2} \(\times\)12cm
= 288cm^{3}
Solution:
Area of base (A) = area of \(\triangle\)ABC
= \(\frac{1}{2}\) \(\times\) 24cm \(\times\) 7cm
= 84cm^{2}
Height of prism (h) = 30cm
Volume of prism (V) = A \(\times\) h
= 84cm^{2} \(\times\) 30cm
= 2520cm^{3}
Solution:
Area of base (A) = area of \(\triangle\)ABC
= \(\frac{1}{2}\) \(\times\) 14cm \(\times\) 8cm
= 56cm^{2}
Height of prism (h) = 25cm
Volume of prism (V) = A \(\times\) h
= 56cm^{2} \(\times\) 25cm
= 1400cm^{3}
Solution:
Area of base (A) = area of triangle
= \(\frac{1}{2}\)\(\times\)12cm\(\times\)9cm
= 54cm^{2}
Height of prism (h) = 18cm
Volume of prism(V) = A\(\times\)h
= 54cm^{2}\(\times\)18cm
= 972cm^{3}
Solution:
Area of base (A) = area of triangle
= \(\frac{1}{2}\)\(\times\)4cm\(\times\)6cm
= 12cm^{2}
Height of prism (h) = 8cm
Volume of prism (V) = A\(\times\)h
= 12cm^{2}\(\times\)8cm
= 96cm^{3}
Solution:
Area of base (A) = area of triangle
= \(\frac{1}{2}\)\(\times\)4.5cm\(\times\)5cm
= 11.25cm^{2}
Height of prism (h) = 8cm
Volume of prism(V) = A\(\times\)h
= 11.25cm^{2}\(\times\)8cm
= 90cm^{3}
Solution:
Area of base(A) = area of \(\triangle\)ABD
= \(\frac{1}{2}\)\(\times\)4cm\(\times\)3cm
= 6cm^{2}
Height of prism = h
Volume of prism (V) = A\(\times\)h
42cm^{3} = 6cm^{2}\(\times\)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
= 112cm^{2}
Solution:
Because the triangle is right angled triangle
a^{2} = 8^{2} + 6^{2}
a^{2} = 64 + 36
a^{2} = 100
a = 10
Lateral surface area = area of 3 rectangles
= 10\(\times\)30+8\(\times\)30+6\(\times\)30
= 720cm^{2}
Solution:
Because the triangle is right angled triangle
a^{2} = 4^{2} +3^{2}
a^{2} = 16 +9
a^{2} =25
a =5
Lateral surface area = area of 3 rectangles
= 5\(\times\)10 + 4\(\times\)10 + 3\(\times\)10
= 120cm^{2}
Solution:
Because the triangle is right angled triangle
AC^{2} = AB^{2} + BC^{2}
AC^{2} = 5^{2} +12^{2}
AC^{2} = 25 +144
AC^{2} =169
AC =13
Area of each face = \(\frac{1}{2}\)\(\times\)5\(\times\)12
= 30cm^{2}
Area of both face = 30cm^{2} + 30cm
= 60cm^{2}
Total surface area = area of both face + area of 3 rectangles
= 60cm^{2}+ 5\(\times\)30 + 12\(\times\)30 + 13\(\times\)30
= 960cm^{2}
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