Question

A rectangle is placed around a semicircle as shown below. The length of the rectangle is
16cm.
Find the area of the shaded region. Use the value
3.14 for π, and do not round your answer. Be sure to include the correct unit in your answer.

Answer 1

@jim_thompson5910 @zepdrix @zephyr141 @CrazyCountryGirl @Compassionate @esshotwired

Answer 2

Radius is 8?

Answer 3

looks like it. drawing is kinda bad. is it really a rectangle? wouldn't it be a square if that circle can fit in it? if so just find the area of a circle. divide that by two then find the area of the square then subtract the area of the half circle from the area of the square. right?

Answer 4

is there any other information?

Answer 5

no

Answer 6

It's not a square. It's a semi-circle and a rectangle.

semi-circle radius is 8.
rectangle is 8 x 16.

Enough information is given.

Answer 7

it a semi circle in a retangle

Answer 8

oh ok. sorry. listen to tkhunny

Answer 9

because the top and bottom are equal in a retangle does it mean it 16 also @tkhunny

Answer 10

yes

Answer 11

ok. here's what you do. find the area of the rectangle first.

Answer 12

ok

Answer 13

once you find that just put it aside for now. next we have to find the area of the semi circle with the radius of 8.

Answer 14

do you know the formula for the area of a circle?

Answer 15

yes A=l*w

Answer 16

It's a rectangle. Two pair of congruent and parallel sides and four right angles. Definitely the same top and bottom and the same right and left. If you have a drawing and no one TELLS you it is a rectangle, that's a horse of a different color.

Answer 17

a=16*_? I don't know the width @tkhunny

Answer 18

it's a semi circle and we're assuming the circle goes to the bottom of the rectangle so so the length of the rectangle is the diameter of the semi circle so half of the diameter is the radius which is also the height of the rectangle.

Answer 19

so your length is just 8.

Answer 20

8*16 is the area of the rectangle

Answer 21

128

Answer 22

is the area

Answer 23

yup. now to find the area of the semi circle. since we have the radius we can find it. what's the Area of a circle going to be?

Answer 24

it should be 1/2

Answer 25

of 128

Answer 26

1/2* pi* r2

Answer 27

the area of a square is 128. put that on the side. next on the to do list is finding the area of a CIRCLE. we're done with the rectangle for now. now lets think about the circle. area of a circle is \[\pi r^2\] now just put the radius into that equation. remember that we know what the radius is since we know that the semi circle's height is also the radius. now use the height for the "r" here.

Answer 28

i got 100.96

Answer 29

ok good. now subtract the area of the circle from the rectangle like so \[A_{rectangle}-A_{circle}=A_{shade}\]

Answer 30

so 128-100.6

Answer 31

128-100.96=27.04

Answer 32

yeah that's the area of the shaded region. you see what we did there?

Answer 33

27.04 cm^2 or cm^3

Answer 34

yeah I see

Answer 35

it's area. it's a length times a length. volume is a length times a length times a length. area is only 2 dimensional. so what would you say the correct units would be?

Answer 36

cm^2

Answer 37

yup!

Answer 38

thank you

Answer 39

you did it! good job! :D