Question

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$\mathtt{\bf{\underline{\red{Need\:full\:explanation\::}}}}$

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☞ choose 1 option. ​

Answer 1

ANS:

B.$10 + 3\pi$

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Answer 2

10 + 3π

Option => B

Given :

Arc SBT is one-quarter of a circle with center R and radius 6.

The length plus the width of the rectangle ABCR is 8.

To Find :

The perimeter of the shaded region.

Solution :

Let's consider the :

AR as - a  & RC as - b

We know that :

$\bigstar\;\boxed{\textbf{Perimeter of Quarter circle}\bf = \dfrac{2\pi r}{4}=3\pi}}}$

So,

• AS = 6 - a
• CT = 6 - b
• AC = RB = 6 (Radius)

Now,

The perimeter of the shaded region :

AS + AC + CT + C (SBT)

So,

⇒ ( 6 - a ) + 6 + ( 6 - b ) + 3π

⇒ 18 - ( a + b ) + 3π

As given,

Length + Width = 8

So,

⇒ 18 - 8 + 3π

⇒ Perimeter of the shaded region = 10 + 3π [ OPTION B ]

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Figure :

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