Find the area of the shaded region, if the rectangle has dimensions 8m and 18m and the circle is
inscribed in the rectangle.
I just need an example on how to solve for this. I'm pretty bad at following without examples and my book doesn't show one.
You did not describe the diagram.
What region is shaded?
how big is the circle, what is its radius ?
anyway:
subtract the area of the circle from the area of the rectangle.
Sorry it wasn't complete. The shaded area is the area outside the circle. No radius was given for the circle. Does that mean that I can get the radius of the circle from the rectangle's dimension?
only if the circle touched both sides of the rectangle. Then the diameter of the circle would be the width of the rectangle.
Take half the diameter to get the radius
To find the area of the shaded region, we can break it down into two parts: the area of the rectangle and the area of the circle.
1. Area of the rectangle:
The rectangle has dimensions 8m and 18m. The formula to calculate the area of a rectangle is given by length multiplied by width. Therefore, the area of the rectangle is:
Area_rect = length × width = 8m × 18m = 144m²
2. Area of the circle:
The circle is inscribed in the rectangle, which means it touches the rectangle at four points. In this case, the circle touches the rectangle at the midpoint of each side.
To find the radius of the circle, we use the fact that it is inscribed in the rectangle. Since the diameter of the circle is equal to the length of the rectangle, the radius will be half the length. Therefore, the radius of the circle is:
Radius = length / 2 = 8m / 2 = 4m
The formula to calculate the area of a circle is given by π (pi) multiplied by the square of the radius. Therefore, the area of the circle is:
Area_circle = π × (Radius)² = π × 4m² = 16π m²
3. Shaded region:
Finally, to find the area of the shaded region, we subtract the area of the circle from the area of the rectangle:
Area_shaded = Area_rect - Area_circle = 144m² - 16π m²
Note that the π symbol represents a mathematical constant, approximately equal to 3.14159. So, the final answer for the area of the shaded region will be in terms of both square meters and π.