Stage Four

Problem No. 13 Housing Units

 

People like to have a view. One way to provide a view from most units is to build them in housing blocks so that from the front, they appear like this:

In a housing block that is 40 units high:

(i) how many units will be in the base?

(ii) how many units will be facing the front?

If it was possible to build a housing block 100 units high:

(i) how many units will be in the base?

(ii) how many units will be facing the front?

Hints:

a) Draw a table

Number of squares in the height	1	2	3	4	5	10	21	25	40	100
Number of squares in the Base
Number of squares in the front

b) Explain to your buddy how you worked out the numbers in the table.

c) Express a relationship between the the height and the base in words.

d) Express this relationship algebraically (let the height be h, the base be b).

 All Stage 4 Problems

Reference: Maths Net 7

Cyril Quinlan/Maree Clark/Glenn Abrahams, McGraw Hill, p240

Lets fill in the table and see what happens...

Number of squares in the height	1	2	3	4	5	10	21	25	40	100
Number of squares in the Base	1	3	5	7	9	19	41	49	79	199
Number of squares in the front	1	4	9	16	25	100	441	625	1600	10000

I hope you can see the patterns:

So the number of squares in the base = twice the height minus 1, or b = 2h - 1.

And the number of squares in the front = the square of the height, or n = h².