MATHEMATICSSurface Area

Lesson Objectives

•The aim of this powerpoint is to help you…

• to review the nets of common 3D shapes

• to apply the methods for finding the area of rectilinear shapes to finding the surface area of common 3D shapes

Cubes

• You should be able to recognise the net of a cube… remember a cube has 6 square faces

• The area of one face = length × width

(in a square these are the same distance!)

• The total surface area of 6 faces =

6 × area of one square…

Example…

• Find the surface area of this cube…

2cm

Net & Surface Area

• One square face = 2 × 2 = 4cm²

• Total Surface area = 6 faces = 6 x 4 = 24cm²

2cm

Cuboids

• A cuboid can have all 3 dimensions different BUT there are still 6 faces.

• All the faces are rectangles and there are pairs that are the same (front & back / two sides / top and bottom) so you can work out the area of each rectangle and know it’s the same for another one!

Example…

• Find the surface area of this cuboid…

2cm

3cm

5cm

FRONT

TOP

RT

Net & Surface Area

• TOP = 2 × 5 = 10cm²• Bottom = same = 10cm²

• FRONT = 3 × 5 = 15cm²• Back = same = 15cm²

• RIGHT = 3 × 2 = 6cm²• Left = same = 6cm²

• Total surface area = 10+10+15+15+6+6 = 62cm²

FRONT

TOP

RT

5cm

2cm

3cm

Did you notice…?

• Did you notice that for the cuboid we just had to multiply each of the 3 dimensions together in pairs?

• Let’s look at another example…

Example 2…

• Find the surface area of this cuboid…

3cm

5cm

8cm

FRONT

TOP

RT

Solution without a net…

• Put the 3 dimensions

(3, 5 and 8) into

3 different pairs

and multiply…

• 3 × 5 = 15cm² (for Right & Left)• 3 × 8 = 24cm² (for Top & Bottom)• 5 × 8 = 40cm² (for Front & Back)• Add 6 faces together = 15+15+24+24+40+40 = 158cm²

3cm

5cm

8cm

FRONT

TOP

RT

Prisms & Cylinders

• Prisms have 2 end shapes. All the other faces are rectangles. For cylinders these end shapes are circles.

• There will be as many rectangles as there are edges to the end shape. For cylinders – just one rectangle whose length is the same distance as the circumference of the circle.

• Calculate the area of one end shape (and double for both ends) and add to this the area of each of the rectangles.

Example…

• Find the surface area of this L-shaped prism…

2cm3cm

6cm

FRONT

TOP

RT1

RT2RT3

5cm

7cm

Net & Surface Area• TOP = 3 × 7 = 21cm²• LT = 7 × 7 = 49cm²• BASE = 6 × 7 = 42cm²• RT3 = 2 × 7 = 14cm²• RT2 = 3 × 7 = 21cm²• RT3 = 5 × 7 = 35cm²

• L-shapes are each 2 rectangles…• FRONT = (3 × 5) + (6 × 2) = 27cm²• BACK = (3 × 5) + (6 × 2) = 27cm²

• Total surface area = 21+49+42+14+21+35+27+27 = 236cm²

6cm2cm

3cm

FRONT

TOP

BACK

LT

BASE

RT3

RT2

RT1 5cm

2cm

7cm

6cm

3cm

5cm

What next?• Print out the notes called PAV4-SArea. Read through

them and make sure you answer any questions.

• Work through the MyMaths lesson and its online homework called Nets, Surface Area found at:

• http://app.mymaths.co.uk/334-resource/nets-surface-area• http://app.mymaths.co.uk/334-homework/nets-surface-area

• Save and complete the worksheet called SArea-S1.xlsx

• Now move on to the PAV5a powerpoint