Question

The diagram shows a semi-circle inside of a rectangle of length of 150m. The semi-circle touches the rectangle a ,b, c. Calculate the perimeter of the shaded region. Give our answer correct to 3 significant figures

Answer 1

Step-by-step explanation:

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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

$= \frac{150}{2}=75 m </p><p></p><p>$

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

$and \: m(arc AB) = \frac{\text{Perimeter of the circle}}{4}=\frac{2\pi r}{4} </p><p>$

$= \frac{2\pi (75)}{4} </p><p>$

$</p><p>= \frac{2(3.14)(75)}{4} </p><p>$

$</p><p>= \frac{471}{4} </p><p></p><p>$

= 117.75 m

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

P = 267.75 ≈ 268 m

$</p><p></p><p>⠀⠀\underline{\bf{\dag} \:\mathfrak{pyaala \: raghu :}} </p><p></p><p>⠀$