Question

Solve this.....................

Answer 1

10 + 3π cm

Explanation:

In the given figure,

• Radius of arc/circle = 6 cm
• Length + width of rectangle = 8 cm

Here, we are asked to find the perimeter of the shaded figure, i.e, SA + AC + CT + Arc SBT.

The perimeter of arc SBT can be found using the formula 2πr/4 [Given ⟶ arc SBT = quarter (¼) of a circle].

So,

2πr/4

= 2π(6)/4

= 12π/4

= 3π cm

Now, from the figure..

SA + AC + CT

= (SR - AR) + AC + (RT - RC)

By, rearranging the terms...

= SR + AC + RT - (AR + RC) ---------> (1)

Again, from the figure, we can see that,

• SR = RT = 6 cm (radii of the same circle)
• AC = RB = 6 cm (radii of the same circle)
• AR + RC = 8 cm (length + width of rectangle)

So, by substituting these values in (1)

SR + AC + RT - (AR + RC)

= 6 + 6 + 6 - (8)

= 18 - 8

= 10 cm

And, the perimeter of the shade figure is,

SA + AC + CT + Arc SBT.

`= \boxed{\tt\:10 + 3\pi \: cm}`

_________

Hope it helps!

`\mathfrak{Lucazz}`

Answer 2

• 10 + 3π units

Explanation:

Take into account that:

• AC = RB as diagonals of rectangle ABCR

Since R is the center and B is on the circle we have:

• AC = r = 6 units

The arc SBT is the quarter of the length of circle:

• SBT = 1/4*2πr = 1/2*6π = 3π units

Find the sum of SA and CT:

• SA + AR = 6 ⇒ SA = 6 - AR
• CT + RC = 6 ⇒ CT = 6 - RC
• SA + CT = 6 - AR + 6 - RC = 12 - (AR + RC) = 12 - 8 = 4 units

So the perimeter of shaded zone is:

• P = 6 + 3π + 4 = 10 + 3π units