The diagram shows a semi circle inside a rectangle of length 150 m. the semi circle touches the rectangle at a b and c. calculate the perimeter of the shaded region.

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 =

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 =

Perimeter of Quarter circle =

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

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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 =

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) =

=

= \

=

= 117.75 m

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

P = 267.75 ≈ 268 m