Answer:
x=28
Step-by-step explanation:
We can use similar triangles and proportions to solve this problem. Put the side of the small triangle over the same side of the larger triangle.
x 42
---------- = ----------
x+10 42+15
Simplify
x 42
---------- = ----------
x+10 57
Using cross products
57x = 42 (x+10)
Distribute
57x = 42x+420
Subtract 42x from each side
57x-42x = 42x-42x +420
15x = 420
Divide each side by 15
15x/15 = 420/15
x=28
Answer: Area of the shaded region is 6.867 square cm
Step-by-step explanation:
The shaded area corresponds to the difference of the area of the rectangle and the area of the semicircle.
Area of the rectangle = 4 times 8 = 32 cm^2
Area of the semicircle = 0.5 * pi * r^2 (where r is the radius, i.e., half of the diameters, i.e., 4 cm). So Area = 0.5*pi*4^2 = 25.133 cm^2
The difference: 32 - 25.133 = 6.867 cm^2 (area of the shaded region)
The sides of a square or rectangle
