This question came from my son. He is Primary 6. Took me quite a while to solve it. Guessed I wasn’t that smart. Siangleng and Seng Yew did it, using different methods. How about you? Try it. Take this challenge and post your answer in the comment box.

Find the shaded area.

Catherine KohJust curious… what’s the answer? I got 114.7 sq. cm

andrewangPost authorhmmm…GOOD try…keep u in suspense first while we wait for a few more entries, ok?

HuongThe shaded area is 114 sq cm.

Mark OngKeep the answers coming in guys!

andrewangPost authorseems that quite a few get 114… hmm..sure?

THAO NCA = shaded area 1

B = shaded area 2

S1 = 1/4 x pi x 400 = 100 x pi = A + B + a2 + a3 (1)

S2 = 1/2 x pi x 100 = 50 x pi = A + a2 (2)

S3 = 1/2 x pi x 100 = 50 x pi = A + a3 (3)

(2) & (3) ==> a2 = a3

S2 = a2 + A –> A = S2 – a2 = 50 x pi – a2

(1) –> B = 100 x pi – (A + a2 + a3)

–> B = 100 x pi – (50 x pi – a2 + a2 + a3)

–> B = 50 x pi – a3

(3) ==> B = 50 x pi – (50 x pi – A) = A (4)

a = 100 – 1/4 pi x 100 =

We have A = 100 – 2 x (100 – 1/4 x pi x 100)

A = 100 – 200 + 50 x pi

A = 50 x pi – 100

Where as in (4) we have B = A

==> Shaded Area = 2 x A = 2 x (50 x pi – 100)

= 100 x pi – 200 (5)

Where as pi = 3.14

(5) ==> Shaded Area = 314 – 200 = 114 sqcm

==> Waiting for the PRIZE !!!

Mark OngWow. Thao! That is a detailed working of your answer! Is it correct? Stay tuned!

Francis Nio-> 1/4 circle – triangle ( visualisation )

-> 100 pi – 200 = 114 2/7 sq cm

andrewangPost authorhmm… a lot of similar answers.. For those that are working on it, same answer doesn’t means correct answer ya! Answers will be revealed shortly.. All are invited – PxC staff, ex-PxC staff, non-PxC staffs..

ArthidI got 20 Sq cm.

ApichartMy answer 36.136 …. correct?

SonnnMy answer :100(pi-200)sq cm . Waitting for lucky draw hehe

CLTEH1. draw a straight line across the square (top right down to bottom left)

2. the straight line will cut through the 2 half-circle

3. the total size of the 2 half-moon-like cutted out area is equal to the oval-like shaded area.

4. so total shaded area = 2 half-moon + the irregular shaded area

5. which is the quarter circle area minus the rectangle cutted inside it.

6.=1/4*PI*20^2 – 1/2*20^2

=314-200

=114 sq cm

EvelynThe answer is 114 cmsq.

The first area is 57 cmsq and the second area is also 57 cmsq.

EvelynArea 1 = (half circle) – (triangle)

= (0.5×3.14x10x10) – (0.5x20x10)

EvelynArea 2 : (quarter big circle) – (3/4 small circle) – ((1/4 small circle)- (area 1))

(0.25×3.14x20x20) – (0.75×3.14x10x10) – ((0.25×3.14x10x10)-57))

57 cmsq

jutamasThe answer is 100 sq.cm.

Mark OngWe are seeing such varied answers! Keep the answers coming in – the results will be out soon!

Winnie kohAns is 114.2cmsq.

raykhanWorking:

Area of Quarter Circle

(3.142 x 20cm^2) / 4 = 314.15926 cm sq

Area of Traingle

20cm^2 / 2 = 200 cm sq

Use Area of Traingle to minus off the area of Quarter Circle will give me the area of the shaded portion.

314.15926cm sq – 200 cm sq = 114.15926 cm sq

Final Answer is 114.15926 cm sq

andrewangPost authorContest has ended. Thanks for the participation. The answer is released and the winner will be announced very soon! Stay tuned.

Look out for the next challenge too! All are welcome!

Alexander0.0114159265358 sq m

AlexanderIt took me between 5 to 10 minutes 🙂