Answer:
the total area is 15.6 square units
Step-by-step explanation:
hello,
you can find the total area dividing the shape into two known shapes
total area= area of the trapezoid +area of the semicircle
then
step one
find the area of the isosceles trapezoid using
[tex]A=\frac{a+b}{2}*h[/tex]
where
a is the smaller base
b is the bigger base
h is theheight
A is the area
let
a=2
b=5
h=4
put the values into the equation
[tex]A=\frac{a+b}{2}*h\\A=\frac{5+2}{2}*4\\A=3.5*4\\A=14[/tex]
Step two
find the area of the semicircle
the area of a circle is given by
[tex]A_{c}=\pi \frac{d^{2}}{4}\\[/tex]
but, we need the area of half circle, we need divide this by 2
[tex]A_{semic}=\frac{ \pi \frac{d^{2}}{4}}{2}\\A_{semic}= \pi \frac{d^{2}}{8}[/tex]
now the diameter of the semicircle is 2, put this value into the equation
[tex]A_{semic}= \pi \frac{2^{2}}{8}\\\\A_{semic}= \pi \frac{1}{2}\\ A_{semic}=\frac{\pi }{2}\\[/tex]
find the total area
total area= area of the trapezoid +area of the semicircle
[tex]total\ area= 14+\frac{\pi }{2} \\total\ area=15.6[/tex]
so, the total area is 15.6 square units
Have a good day.
