**In the figure, ABCD is a square with a perimeter of 84 cm. It is made up of identical squares and quarter-circles. ****a) Find the perimeter of the shaded region.b) Find the area of the shaded region.**

**Solution**

**a)**

The perimeter of square ABCD is 84 cm.

1 side of square ABCD ----- 84 cm divided by 4 = 21 cm

Radius of the 6 quadrants ----- 21 cm divided by 3 = 7 cm

The shaded area is made up of 6 quadrants -----

6 x ¼ x 2 x 22/7 x 7 cm =

**66 cm (Answer)**

**b)**Redrawing the figure….

Area of 1 quadrant -----

¼ x 22/7 x 7 cm x 7 cm = 38.5 square cm

Area of 1 small partially shaded square ----

Area of 1 small square – Area of 1 quadrant ----- (7 cm x 7 cm) – 38.5 square cm = 10.5 square cm

Area of 2 such small partially shaded squares -----

10.5 square cm x 2 = 21 square cm

Area of 3 small shaded squares -----

(3 x 7 x 7) square cm = 147 square cm

Total shaded area ------

(21 + 147) square cm =

**168 square cm (Answer)**

## 3 comments:

Dear Mr Song

I noticed that the answers for these two questions in the cbox are different

Both these questions looked similar at first glance. Could you help to clarify the reason? 10 % more and 10% lighter? Quite confusing for P6 students.

teq: A has 10% more than B.B has 10% more than C .what is the diffrence between A and C ? a) 20% b)21% C) 30% d)31%

Excel to teq: Percentage Q, answer is (b).

Confused: Hi Mr Song, pls help me.Azizah is 10 % lighter than Bala. Bala is 10 % lighter than Caili.How many percent is Azizah lighter than Caili ? TQ.

Excel: To confused :- That Q has now become a Short Q rather than Sect C Q in most schools. Answer is 19%.

C ----- 100%

B 10% more ----- 100% + 10% = 110%

A 10% more than B ----- 110% + 11% = 121%

C more than A ----- 121% - 100% = 21%

Caili ----- 100%

Bala 10% lighter ---- 100% - 10% = 90%

Azizah 10% lighter than Bala ----- 90% - 9% = 81%

Azizah lighter than Cailing ----- 100% - 81% = 19%

Dear Mr Song

Thank you for your advice.

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