Respuesta :

Answer:

Perimeter of the shaded region is 268 m

Step-by-step explanation:

In this diagram a semi circle is drawn inside a rectangle of length 150m.

Length of diameter of a semicircle = 150 m

So radius of the semicircle = [tex]\frac{150}{2}=75 m[/tex]

We have to find the perimeter of the shaded region.

Perimeter of the shaded region = length of tangents drawn on the circle at A and B + m(arc AB)

Length of tangents = radius of the semi circle = 75 m

and m(arc AB) = [tex]\frac{\text{Perimeter of the circle}}{4}=\frac{2\pi r}{4}[/tex]

= [tex]\frac{2\pi (75)}{4}[/tex]

= [tex]\frac{2(3.14)(75)}{4}[/tex]\

= [tex]\frac{471}{4}[/tex]

= 117.75 m

Now Perimeter of the shaded region = 75 + 75 + 117.75

P = 267.75 ≈ 268 m

akposevictor

Given the image showing a rectangle that is 150 cm long with a semicircle inside of it, the perimeter of the shaded region is:  267.8 m

Recall:

Perimeter of a circle = [tex]2 \pi r[/tex]

Thus, given the semicircle in the diagram below, where:

Length of rectangle = 150 m

Radius of semi circle = half of 150 m = 75 m

Thus,

The width of the circle = 75 m

The shaded region is bounded by the circumference of a quarter circle (AB) and two sides measuring 75 m each.

Perimeter of Quarter circle = [tex]\frac{1}{4} \times 2 \pi r[/tex]

  • Substitute

Perimeter of Quarter circle = [tex]\frac{1}{4} \times 2 \times \pi \times 75 = 117.8 m[/tex]

Perimeter of the shaded region = 117 + 75 + 75 = 267.8 m

Learn more here:

https://brainly.com/question/18869010

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