Surface Area of Prisms

OCR Stage 8

A PrismCylinder

Cuboid

Triangular PrismTrapezoid Prism

Surface Area of Prism = Total of ALL individual surfaces

Area Formulae

Area Circle = π x r2

r

Area Rectangle = Base x height

h

b

b

h

Area Triangle = ½ x Base x height

h

b

Area Trapezium = ½ x (a + b) x h

a

Surface Area Cuboid

5.3cm

7.2cm

10.6cm

Area A = b x h

= 7.2 x 5.3= 38.16cm2

BUT there are 2 A’s, 2 B’s and 2 C’s

AB

C

Area B = b x h

= 5.3 x 10.6= 56.18cm2

Area C = b x h

= 7.2 x 10.6= 76.32cm2

2 x A = 38.16 x 2 = 76.32cm2

2 x B = 56.18 x 2 = 112.36cm2

2 x C = 76.32 x 2 = 152.64cm2

Total Surface Area = 341.32cm2

5cm

3cm

Cross-sectional Area = π x r2

= π x 32

= 28.2743…..cm2

Curved surface area = 5 x 2 x π x 3

Total = 56.5486… + 94.2477..= 154.796..cm2 = 154.8cm2

= 94.2477….cm3

Surface Area of Cylinder

2πr

5

2 x Circles = 2 x 28.2743… = 56.5486… cm2

Surface Area - Trapezoid PrismCross-sectional Area = ½ x(a + b) x h

= ½ x (6.3 + 1.7) x 4.9

1.7cm8.2cm

6.3cm

4.9cm= 19.6cm2

A

BC

2 x A = 19.6 x 2 = 39.2cm2

2 x B = 8.2 x 4 x 2 = 65.6cm2

1 x C = 8.2 x 6.3 = 51.66cm2

Total Surface Area = 170.4cm2

4cm

D (the base)

1 x D = 8.2 x 1.7 = 13.94cm2

Surface Area Triangular PrismCross-sectional Area = ½ x b x h

= ½ x 8.6 x 4.1

DO NOT ROUND!

8.6cm6.2cm

4.1cm 4.9cm= 17.63cm2

AB

C [rear]

D [the base]2 x A = 17.63 x 2 = 35.26cm2

1 x B = 6.2 x 9.53 = 57.18cm2

1 x C = 4.1 x 6.2 = 25.42cm2

Total Surface Area = 171.48cm2

1 x D = 8.6 x 6.2 = 53.32cm2

9.53cm