Answer:
20.52cm^2
Step-by-step explanation:
from the picutre we can see that this is a semicircle with 2 right angle triangles inside it. to find the area we will solve for the semi circle then solve for the triangles and and subtract
circle area is [tex]\pi r^{2}[/tex] leaving the semicircle to be [tex]\frac{\pi r^{2} }{2}[/tex] for the semi circle
next we need the radius. since the diameter is given, we can solve for r by dividing it in two
12 ÷ 2 = 6
so the area of the semi circle is [tex]\frac{\pi 6^{2} }{2}[/tex]
this gives 18[tex]\pi[/tex]cm^2 if we simplify
next the triangles, since they are equal in size we can treat them as a square and stack them. this is because they have equal side lengths so when stacked they form a square:
base x height divided by 2 times 2 would be the normal process to find two equal triangles but you can see the division and multiplication cancel out
6x6= 36cm^2
finally subtracting the areas to find the shaded region and use 3.14 as pi
18[tex]\pi[/tex]cm^2 - 36cm^2 = 20.52cm^2
