Gem ToF - Part 2

Geometry Level 1

True or False

The red area and the orange area are equal

False, the red area is larger False, the orange area is larger True

2 solutions

Rohit Ner
Jul 11, 2015

Let $r$ be the radius of the quarter circle.
$\begin{aligned}\Rightarrow B+D&=\pi \frac{{(\frac{r}{2})}^2}{2}\\&=\pi\frac{{r}^{2}}{8} A+B+C+D&=\pi\frac{{r}^{2}}{4}\\A+C&=\pi\frac{{r}^{2}}{8}\\\Rightarrow A+C&=B+D \end{aligned}$
But by symmetry
$\begin{aligned}C&=D\\\Rightarrow A&=B\end{aligned}$

Hm, I don't quite understand your second equation. Is there a formatting error?

Is there another way to see this result?

Chung Kevin - 5 years, 11 months ago

A+B+C+D should have been written separate from the above equation. He just mean the area of the whole quarter circle A+B+C+D=pi*(r^2)/4

Radinoiu Damian - 5 years, 10 months ago

Hadia Qadir
Jul 22, 2015

Let the radius of the quarter be R . the area of the quarter circle is S= pi^/4

Let the area of the white region be (1) and (2) the red region be (3) and the orange be (4) =(1)+(4)=(2)+(3) Because (1) = (2) piR^2/8-3 = (3) = (4)

The red area and the orange area are equal

Gem ToF - Part 2

2 solutions

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