Explanation:
#6
it is an isoceles trapezoid minus the inner circle with radius 1 mile (half of the given diameter of 2 miles).
the area of the trapezoid is
height × (long baseline + short baseline)/2 =
= 2 × (4 + 2)/2 = 4 + 2 = 6 mi²
the area of the circle is
pi×r² = pi×1² = pi mi²
the shaded area is then
6 - pi mi² ≈ 6 - 3.14 mi² ≈ 2.86 mi²
and to be safe
#5
it is the circle minus the rectangle.
the area of the circle is
pi×r² = pi×6² = 36pi mm² ≈ 36×3.14 ≈ 113.04 mm²
the area of the rectangle is
10×1.5 = 15 mm²
the shaded area is then about
113.04 - 15 = 98.04 mm²