A semicircle is inscribed in a rectangle with area 144 square centimeters. In square cm, what is the area of the semicircle?

The question does not make sense.

You can construct an infinite number of
rectangles that have an area of 144 cm².

141 cm x 1 cm

72 cm x 2 cm

36 cm x 4 cm etc.

They say it is 36Pi sq.cm

If whole semicircle lie in rectangle then width is equal radius of semicircle.

W = r

Length is equal diametar of semicircle.

L = d = 2 r

Area of rectanlgle:

A = L ∙ W

144 = 2 r ∙ r

144 = 2 r²

Divide both sides by 2

72 = r²

r² = 72

Area of circle:

A = r² ∙ π

Area of semicircle:

A = r² ∙ π / 2

A = 72 ∙ π / 2

A = 36 π cm²

To find the area of the semicircle, we need to determine the radius of the semicircle first.

Let's denote the width of the rectangle as 'w' and the length as 'l'.

Since the semicircle is inscribed in the rectangle, the diameter of the semicircle is equal to the width of the rectangle. Therefore, the diameter of the semicircle is 'w'.

We know that the formula for the area of a semicircle is A = (π * r^2) / 2, where 'A' is the area of the semicircle and 'r' is the radius.

In this case, the radius is half of the diameter, so the radius of the semicircle is 'w/2'.

Now we can substitute the values into the formula to find the area of the semicircle:

A = (π * (w/2)^2) / 2

Before we proceed further, we need to find the value of 'w'.

The given rectangle's area is 144 square centimeters, so we have:

w * l = 144

Since we don't have the value for 'l', we need more information to solve for 'w' accurately.