Answer:
The shaded part is 17.875 in².
Step-by-step explanation:
To calculate the area of the shaded part,
- Calculate the area of the circle
- Calculate the area of the triangle
- Calculate the area of the rectangle (which has the circle and triangle in it)
- Subtract the areas for circle and triangle from area of the rectangle
Area of the circle
A = πr²
Find the radius (r), which is half the diameter.
r = d/2
r = 5/2
r = 2.5
Substitute the radius into the formula. I will round pi to 3.14.
A = πr²
A = (3.14)(2.5²)
A = 19.625
The area of the circle is 19.625 in².
Area of the triangle
A = (bh)/2
The base and height are the same as the diameter.
Substitute the base and the height.
A = (bh)/2
A = (5 x 5)/2
A = 25/2
A = 12.5
The area of the triangle is 12.5 in².
Area of the rectangle
A = lw
The length is double the diameter (l = 2d = 10) and the width is 5 (w = 5).
Substitute the length and the width.
A = lw
A = 10 x 5
A = 50
The area of the rectangle is 50 in².
Area of the shaded part
A = rectangle - white
A = rectangle - (circle + triangle)
Substitute the areas for the shapes.
A = rectangle - (circle + triangle)
A = 50 - (19.625 + 12.5)
A = 17.875
Remember the include the units:
17.875 in²
