Answer:
e) Area of shaded part = a^2(1 - 0.25 π). Radius of the arc = 0.5a.
f) Area of shaded part = 0.5a^2( π - 2). Radius of the arcs = a.
Step-by-step explanation:
e) Area of shaded part = area of the square - area of the 2 semicircles
= a^2 - 2 * 0.5 π r^2
= a^2 - π (0.5a)^2
= a^2 - 0.25 a^2 π
= a^2(1 - 0.25π )
The radius of the semicircle is 0.5a.
f) Split the shaded area into 2 parts by drawing the diagonal of the square through the shaded area.
The area of one half = the area of the quarter circle - area of the triangle formed by the diagonal
= 0.25 π a^2 - 0.5a^2
= 0.25 a^2 π - 0.5a^2
= 0.25a^2( π - 2)
So the total area of the shaded area
= 2 * 0.25a^2( π - 2)
= 0.5a^2( π - 2).
