**Question**

**Introduction**

This is
another “Bonus Question” at a secondary level from somewhere that the question
poser did not mention, but I guess it is most likely an Integrated Programme
school in Singapore . It is a beautifully crafted question. The presence of a slant line seems to necessitate
the usage of Pythagoras’ Theorem. However,
we have seen that Pythagoras’ Theorem can actually be avoided even in Primary
(Elementary) School problems. So a 10
year old kid with a rudimentary knowledge of algebra could do this. Can you spot a short cut?

**Making Observations**

Stare at
the diagram for a while. What do you observe?

**Solution**

area of D

*DB*= ½ of the area of_{n}C_{n}*AB*._{n}C_{n}D
area
of D

*DB*= ½ of the area of_{n}C_{n}*DB*._{n}PQ
\ area of

*DB*= area of_{n}PQ*AB*=_{n}C_{n}D*n*cm^{2}.
H04. Look for pattern(s)

H05. Work backwards

H09. Restate the problem in
another way

H11. Solve part of the problem

**Suitable Levels**

*****Lower Secondary Mathematics

*****challenge for Primary school Olympiad

* other syllabuses that involve areas and a
tiny bit of algebra

* anyone game itching for a challenge

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