Square in a circle and two squares

Geometry Level 3

Two 4 x 4 squares intersect at right angles, bisecting their intersecting sides, as shown. The circle's diameter is the segment between the two points of intersection. What is the area of the shaded region created by removing the circle from the square?

16 – 2π 32 – 2π 16 – 4π None of these 28 – 2π 28 – 4π

2 solutions

Mahdi Raza
Jul 18, 2020

$\Large{\boxed{28-2\pi}}$

Nice picture! It explains well why to remove that 4-area!

Vinayak Srivastava - 10 months, 4 weeks ago

A Former Brilliant Member
Jul 18, 2020

The area of the region bounded by the squares is $4^2+4^2-2^2=28$ square units

Area bounded by the circle is $π\times (\frac{2}{\sqrt 2 })^2=2π$ square units

Hence the required area is $\boxed {28-2π}$ square units.

Oh I forgot to remove the $2^2$ ! Nice solution, Sir!

Vinayak Srivastava - 10 months, 4 weeks ago

Yeah, removing that intersection is crucial as well!

Mahdi Raza - 10 months, 4 weeks ago