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2 years ago

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

Mathematics

2 answers:

Masja [62]2 years ago

8 0

Answer:

10 + 3π cm

Step-by-step 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!

$\mathfrak{Lucazz}$

scoray [572]2 years ago

5 0

Answer:

10 + 3π units

Step-by-step 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

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