Basic mathematics-problem solving.Area and diameter of 2-D shapes.

Written by : Normaisyarah bt. Zainudin

Nur Syahmi bt. NazriHasliza bt Julaihi

Tan Pei PingLoong Lee Ying

2 PPISMP Mathematics

Question :

Construct all the possible shapes by joining 9 unit square tiles.

(a) What can you say about the area of

all the shapes?

(b) Which shape has the minimum

perimeter?

(c) Make a conjecture about the shape

with the minimum perimeter.

Area is weight x height

A = W x H

= 1cm x 1cm

= 1cm

Therefore, the area for 9 unit square tiles are 9cm

The area for all shape is same even though the

shape is not same but as it has same unit, so the

area will same.

1cm

1cm

2

2

The conjecture for 9 unit square tiles are :

No: Conjecture: Perimeter:

1

2

3

4

20cm

20cm

18cm

16cm

No: Conjecture: Perimeter:

5

6

7

14cm

12cm

36cm

No: Conjecture: Perimeter:

8 36cm

Based on all the conjecture above,

has maximum perimeter (36cm) and

has minimum

perimeter

(12cm).

The conjecture for 5 unit square tiles are :

No: Conjecture: Perimeter:

1

2

3

12cm

12cm

10cm( minimum perimeter )

20cm( maximum perimeter )

The conjecture for 8 unit square tiles are :

No: Conjecture: Perimeter:

1

2

3

4

18cm

18cm

16cm( minimum perimeter )

20cm( maximum perimeter )

No: Conjecture: Perimeter:

5

6

7

12cm( minimum perimeter )

12cm

16cm

32cm( maximum perimeter )

As a conclusion, we can conclude that the shape which is compact has minimum perimeter and the shape which is only join each other at the corner has maximum perimeter.

We can test this hypothesis by joining 5 unit square tiles, 8 unit square tiles, 10 unit square tiles, 11 unit square tiles, 16 unit square tiles and also 25 unit square tiles. Just imagine how we want construct it one by one. We only wasting our time as the result is same.

Even though there are different number of tiles, but we can conclude it has the same shape for minimum and maximum perimeter as we can see in page 7.