The perimeter of a semicircle is 72 cm. Find the raduis of the semicircle and then find its area
Consider the full circle: perimeter 144
radius= perimetercircle/2PI
areacircle= PI*rad^2
areasemicircle= 1/2 area circle
To find the radius of the semicircle, we can first find the radius of the full circle.
The perimeter of the full circle is given as 144 cm.
The formula for the perimeter (circumference) of a circle is given by P = 2πr, where P is the perimeter and r is the radius.
Substituting the given value, we have 144 = 2πr.
To find the radius, we can rearrange the equation:
r = P / (2π)
r = 144 / (2π)
r ≈ 22.92 cm
Now that we have the radius of the full circle, we can find the area of the semicircle.
The formula for the area of a circle is given by A = πr^2, where A is the area and r is the radius.
The area of the semicircle is half the area of the full circle, so we multiply the area of the full circle by 1/2.
Area of the semicircle = 1/2 * π * r^2
Area of the semicircle ≈ 1/2 * π * (22.92 cm)^2
Area of the semicircle ≈ 329.16 cm^2
Therefore, the radius of the semicircle is approximately 22.92 cm and the area of the semicircle is approximately 329.16 cm^2.