Explanation:
as the graphic shows, it is a combination of
a rectangle
a right-angled triangle
a half-circle
the area of the composite figure is simply the sum of the individual areas.
the area of a rectangle is
length × width
in our case
Ar = 6 × 3 = 18 cm²
the area of a triangle is
baseline × height / 2
for a right-angled triangle both legs are used as baseline and height.
so, in our case
At = 6 × 8 / 2 = 6 × 4 = 24 cm²
the area of a circle is
pi × r²
"r" being the radius (= half of the diameter).
the area of a half-circle is then
pi × r² / 2
in our case the diameter is 8 cm, so, r = 8/2 = 4 cm and we get
Ac = pi × 4² / 2 = 3.14 × 16 / 2 = 25.12 cm²
so, the total area is approximately
18 + 24 + 25.12 = 67.12 cm²