Question

Find the area of the shade region if d=18 units. Round to the nearest tenth.

Answer 1

Answer:

29.3 units^2

Step-by-step explanation:

sorry for no explanation

Answer 2

Answer:

Area of shaded region = 254.5 square units

Step-by-step explanation:

We have 3 semicircles:

d = 18 units

Semicircle 1 = The big semicircle

Semicircle 2 and 3 = The two small semicircles

Semicircle 2 = 18 units

Semicircle 3 = 18 units

Semicircle 1 = Semicircle 2 + Semicircle 3 = 36 units

Radius = Half of the diameter

Semicircle 1 radius = 18 units

Semicircle 2 radius = 9 units

Semicircle 3 radius = 9 units

$\mathrm{Area\:of\:a\:semicircle = \dfrac{ \pi r^2 }{ 2 }}$

$\mathrm{Area\:of\:shaded\:region = Area\:of\:Semicircle\:1 - (Area\:of\:Semicircle\:2 + Area\:of\:Semicircle\:3)}$

$\mathrm{Area\:of\:shaded\:region = \dfrac{ \pi r^2 }{ 2 } - ( \dfrac{ \pi r^2 }{ 2 } + \dfrac{ \pi r^2 }{ 2 } )}$

$\mathrm{Substitute\:the\:numbers\:into\:the\:equation}$

$\mathrm{Area\:of\:shaded\:region = \dfrac{ \pi (18)^2 }{ 2 } - ( \dfrac{ \pi (9)^2 }{ 2 } + \dfrac{ \pi (9)^2 }{ 2 } )}$

$\mathrm{Do\:all\:of\:the\:exponents\:first}$

$\mathrm{Area\:of\:shaded\:region = \dfrac{ \pi\times324 }{ 2 } - ( \dfrac{ \pi\times81}{ 2 } + \dfrac{ \pi\times81}{ 2 } )}$

$\mathrm{Combine\:\dfrac{ \pi\times81}{ 2 }\:and\:\dfrac{ \pi\times81}{ 2 }\:to\:get\:\pi\times81}$

$\mathrm{Area\:of\:shaded\:region = \dfrac{ \pi\times324 }{ 2 } - ( \pi\times81 )}$

$\mathrm{Divide\: \pi \times324\:by\:2}$

$\mathrm{Area\:of\:shaded\:region = { \pi\times162} - \pi\times81}$

$\mathrm{Combine\:\pi \times162\:and\:- \pi \times81}$

$\mathrm{Area\:of\:shaded\:region = 81\pi}$

$\mathrm{Area\:of\:shaded\:region = 254.469004941}$

Area of shaded region rounded to the nearest tenth is: 254.5 square units

look at the picture for more information