**Question**

**Introduction**

This looks
like a challenging problem regarding area.
The diagram looks very confusing.
The shaded area consists of many convex pieces. Furthermore, the unshaded regions comprise
triangle-like pieces of which we do not know all the dimensions. The only dimensions we know is related that
of the large triangle D

*ACB*. What shall we do?
The key to
solving this problem is to appropriately cut up the figure so as to be able to
“see” it properly. We can cut up the
figure like this:-

You
might note that the pink triangles and green triangles are right-angled
triangles, because they are in semi-circles.
Yeah! Smart! But how can this be useful? We do not know their individual bases and
heights. We only know their longest
sides. Hmmmmm ... Ah! However,
the pink triangles and
green triangles all add up to the large triangle D

*ACB*. This is a key observation.
Note that the convex parts can be viewed
as semi-circles with either a pink triangle or green triangle taken away. There are two pairs of semi-circles: one
large and one small. Therefore, the
shaded area is the total of one small circle plus one large circle minus the total
of the areas of the pink and green triangles (which is the same as the area of
triangle D

*ACB*). As you know, the area of the triangle D*ACB*is ½ ´ base ´ height, in which ½ ´ base = 5 cm. Once you understand all these, the calculation is very easy.**Solution**

total area of
shaded regions

= area of large circle + area of small circle – area of
triangle D

*ACB*
= [

*p*(5)^{2}+*p*(^{5}/_{2})^{2}– 5 ´ 10] cm^{2}
= 48.18 cm

^{2}
H02. Use a diagram / model

H04. Look for pattern(s)

H09. Restate the problem in
another way

H10. Simplify the problem

H11. Solve part of the problem

**Suitable Levels**

*****Primary School Mathematics

* other syllabuses that involve area of triangles and circles

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