Suppose a square ABCD has a side length of 1 unit. The arcs BD and AC are circular arcs with centers at A and D, respectively. Find the area of the shaded region.

Question

asked Mar 22, 2021 678 views

1 Answer

Anthony Akentiev · Answer 1 · 2021-03-29T05:47:47+0000

Answer:

$1-(√(3) )/(4)-(\pi)/(6)$

Explanation:

The missing figure is shown in the attachment

The area of the shaded region = Area of Square - (Area of sector AOB + Area of equilateral triangle BOC + Area of sector COD)

Area of Sector AOB=Area of Sector COD=
$(30)/(360)*\pi*1^2=(\pi)/(12)$

Area of equilateral triangle =
(1)/(2)*r*(√(3) )/(2)*r= (1)/(2)*1*(√(3) )/(2)*=(√(3) )/(4)

Area of shade region =
$1^2-(√(3) )/(4)-(\pi)/(12)*2$

$1-(√(3) )/(4)-(\pi)/(6)$