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