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}