Question

ABCD and EFGH are squares. if JH=4 cm and JC=9 cm, then what is the area of the shaded region?

Answer 1

I'm not sure if this is right, but i think you double 9cm...

Answer 2

and then you would have to multiply

Answer 3

@nikato and @Compassionate
for additional help

Answer 4

and then you would multiply the sides

Answer 5

I hope that made sense'

Answer 6

can you explain it a lil more please?

Answer 7

So essentially once you add/double the number 9 you will have one line essentially,

Answer 8

First you want to find the area of the big square.

Triangle BJC is an isosceles right triangle. Agree?
With right angle BJC and BJ=9=JC

Answer 9

and that line is AC (basically u will have figured out that line segment ( i believe it is called that)

Answer 10

Then using pythagoereom theorem.
9^2 +9^2= BC^2
So solve for BC which will the length of one side of the big square

Answer 11

9^2+9^2=162

Answer 12

now what

Answer 13

Well BC is actually = sqrt162 which can be simplify to 9sqrt2

Answer 14

So now that you know BC=9sqrt2. That means all 4 sides are also that length

To find the area, (9sqrt2)^2
And that equals 162
So the area of the big square is 162

Answer 15

Do the same for the small square.
EJH would be one of the right isosceles triangle.
So use pythagoereom theorem to find one of the sides, EH
4^2 +4^2 =EH^2
So what's EH?

Answer 16

^

Answer 17

sqrt32?

Answer 18

Correct
And to find the area of the small square it'll be the square of the sides so

(Sqrt32)^2=area of small square
So area=32
To find the shaded region
Subtract the big with the small area

Answer 19

130

Answer 20

YES. Great job!