Step-by-step explanation:
Given : A rectangle 4 x 8 , a semicircle
Diagonal intersecting semicircle  
To Find :Area of red part
<h3>Solution:</h3>
Angle AC make AB   α = ∠BAC
tan α = BC/AB = 4/8 = 1/2
=> α = 26.565°
 ∠ECA = ∠BAC = α
EC = EF = 4
=> ∠CEF = 180° - 2α
∠AED = 45°  as   AE is  diagonal of Square of side  4
=> ∠AEF  + 180° - 2α + 45° = 180°
=>  ∠AEF =  2α - 45°  = 8.13°
in Left side area  between square  and circle is split in 2 Equal parts 
(1/2) area - area AFG = area of Red part
in Left side area  between square  and circle  = 4² - (1/4)π4²
= 3.4336 sq unit 
half  =  1.7168 sq unit  
Now find area AFG = area ΔAEF - sector EGF
area ΔAEF  
AE = 4√2  , EF = 4    angle = 8.13°
area ΔAEF   = (1/2) 4√2 * 4 sin 8.13° = 1.6 sq unit
area  sector EGF  = (8.13/360)π4² = 1.135  sq unit
 area AFG  = 1.6 - 1.135  = 0.465 sq unit
 Area of Red part = 1.7168 - 0.465 sq unit
= 1.2518 sq unit
= 1.252  sq unit
= 1.25 sq unit.
Hope this helps!!