Is the area of a semicircle with a diameter of x greater than, less than, or equal to a circle with a diameter of 12x? Explain.

Area of circle with a diameter of 12x is greater than area of a semicircle with a diameter of x

Step-by-step explanation:

Since semicircle is half of the full  circle, then area of semicircle is also half of the full  circle.

Area of circle is given by

therefore, area of semicircle is

Also radius for any circle is half of diameter

radius = Diameter/2

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For semicircle

Diameter = x

Radius = x/2

area of semicircle is given below

area of semicircle is

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For circle

Diameter = 12x

Radius = 12x/2 =6x

area of circle is given below

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we can see that

area of semicircle is

and

area of circle is

Hence, area of circle with a diameter of 12x is greater than area of a semicircle with a diameter of x

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step-by-step explanation:

step-by-step explanation:

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