To find the area of the shaded region, we first need to find the area of the whole circle and then subtract the area of the quarter circle that is not shaded.
Area of a circle = πr^2, where r is the radius
Radius (r) = 5cm
Area of circle = π(5)^2 = 25π cm^2
Since there are 4 equal quarters, each quarter circle has an area of (1/4) * 25π = 6.25π cm^2
Next, we need to find the area of the quarter circle that is not shaded. We first need to find the central angle of the shaded quarter, which is 90 degrees.
The area of a circle sector = (central angle/360) * πr^2
Area of the shaded quarter = (90/360) * π(5)^2 = 6.25π cm^2
Therefore, the area of the shaded region is:
25π cm^2 - 6.25π cm^2 = 18.75π cm^2
So, the area of the shaded region is 18.75π square centimeters.
Find the area of the shaded region. Be sure to show your work and answer with units. It is a circle with a 5cm apothem and cut into 4 equal quarters and one of the quarters has a line draw at the bottom of it to make it look like a triangle.
3 answers
the whole quarter isn't shaded only the bottom of it is to make it look like a triangle
I apologize for the misunderstanding. Let's find the area of the shaded region correctly.
The area of the shaded region can be split into the area of the quarter circle and the area of the triangle formed by the shaded portion of the quarter circle.
1. Area of the quarter circle:
Radius of the circle (r) = 5 cm
Area of quarter circle = (1/4) * π * r^2 = (1/4) * π * 5^2 = 6.25π cm^2
2. Area of the triangle:
Since the triangle is formed by the shaded portion of the quarter circle, the base of the triangle is equal to the radius of the circle, which is 5 cm. The height of the triangle is also 5 cm because it is an apothem.
Area of the triangle = (1/2) * base * height
Area of the triangle = (1/2) * 5 * 5 = 12.5 cm^2
3. Total area of the shaded region:
Total area = Area of quarter circle - Area of triangle
Total area = 6.25π cm^2 - 12.5 cm^2 = 6.25π - 12.5 cm^2 = approximately 6.96 cm^2
Therefore, the area of the shaded region is approximately 6.96 square centimeters.
The area of the shaded region can be split into the area of the quarter circle and the area of the triangle formed by the shaded portion of the quarter circle.
1. Area of the quarter circle:
Radius of the circle (r) = 5 cm
Area of quarter circle = (1/4) * π * r^2 = (1/4) * π * 5^2 = 6.25π cm^2
2. Area of the triangle:
Since the triangle is formed by the shaded portion of the quarter circle, the base of the triangle is equal to the radius of the circle, which is 5 cm. The height of the triangle is also 5 cm because it is an apothem.
Area of the triangle = (1/2) * base * height
Area of the triangle = (1/2) * 5 * 5 = 12.5 cm^2
3. Total area of the shaded region:
Total area = Area of quarter circle - Area of triangle
Total area = 6.25π cm^2 - 12.5 cm^2 = 6.25π - 12.5 cm^2 = approximately 6.96 cm^2
Therefore, the area of the shaded region is approximately 6.96 square centimeters.
3 answers