Question

Hi,

This is Q2 from P6 OnSponge Conquer Problem Sums’ unit 3.4 that’s teaching Cut and Paste method on circles. Don’t quite understand the answer that’s given. No diagram was given, but just answer: “area of share part ->1 big semi circle =½*πr²=½*π(12)²≅226 cm².

How is this being arrived at?

Source: Assessment

Hi SAHMom,

Awesome visualising skills! Very creative!

The original diagram in the OnSponge book is not drawn so well. Won’t be able to draw to show these congruencies like what your diagram here shows when you draws the triangles.

Thanks so much!

0 Replies 1 Like ✔Accepted Answer

Consider filling up the blank areas in the centre:

(1) flipping the grey+blue area into blank space (blue)

(2) moving the grey+red “leaf” into blank space (red)

(3) moving the grey+pink “leaf” into blank space (pink)

We get a completely filled up semi-circle.

Hi SAHMom,

Awesome visualising skills! Very creative!

The original diagram in the OnSponge book is not drawn so well. Won’t be able to draw to show these congruencies like what your diagram here shows when you draws the triangles.

Thanks so much!

0 Replies 1 Like ✔Accepted Answer