Question

What is the perimeter of this composite figure?





16.56 in.

14.28 in.

18.28 in.

10.28 in.

Answer 1

Okay, first we must find the perimeter of the circle, which is the 2 semi-circles together. since the inside figure is a square with side lengths 2, the diameter of the circle is 2

Answer 2

that makes sense?

Answer 3

Yes.

Answer 4

The formula for circumference of a circle is C=2pi r which is the same as pi* the diameter
use your calculator to find pi*2

Answer 5

6.28

Answer 6

Great! now the only part we are missing is the square, since only 2 of the sides are on the outside, instead of multiplying the side length by 4 we only multiply it my 2,
2*2=4 add this to the circumference of the circle and you get the total!

Answer 7

Okay, im confused with the last part.

Answer 8

Okay, You are finding the distance around the figure correct?

Answer 9

Yes.

Answer 10

I will show you the first part that we calculatedc http://prntscr.com/42obok
we already calculated the part I outlined in red

Answer 11

We must calculate the distance of these 2 lines on the bottom of the heart

Answer 12

okay.

Answer 13

This is easier than the last part, what is 2+2?

Answer 14

4

Answer 15

Yes exactly! so if the perimeter of the bottom part of the heart is 4, and the top is 6.28, you simply add them together to find the total perimeter

Answer 16

How would you find the area? Wouldnt you use the parralelogram formula?

Answer 17

You want to find the area of the same figure as before?

Answer 18

YEs

Answer 19

Okay, first what is the formula for area of a square?

Answer 20

p=4s

Answer 21

right?

Answer 22

That is the perimeter, To find the area you multiply the length of a square with the width of the square,
A=L*W but in a square the length and width are the same so we only need one side length. Can you find that in the figure?

Answer 23

You would do 2 x 2 ?

Answer 24

Yes that is the area of the square part of the heart.
Now we have solved for this part of it : http://prntscr.com/42oerv

Answer 25

But we still need to find the area of the top part
The area of a circle Is A=pi(r)^2

Answer 26

6.28

Answer 27

Not quite. The radius is different from the diameter
the radius is only half of the length of the diameter. since we already said the diameter = 2, what is the raidus?

Answer 28

1

Answer 29

Yes so the area of the circle is not 6.28, but 1pi.. what does that =?

Answer 30

3.14

Answer 31

Yes correct! so now much like the last one we add the 2 parts together to find the area. WE found that the area of the bottom part is 4 and the top part is 3.14
What is 4+3.14?

Answer 32

3.18?

Answer 33

no wait 7.14

Answer 34

Yep 7.14 is correct :)