Question

http://prntscr.com/jgsx9s Geometry help

Answer 1

@Elsa213

Answer 2

it's blank

Answer 3

we use the square area formula?

Answer 4

We find the area of the square then subtract out the area of the triangles that are not shaded.

Answer 5

Pretty easy to do, just hang on a minute.

Answer 6

Okay, so basically, now we can easily find the area of the square, then find the areas of each triangle then perform the following calculation:
\(\text{Area of Shaded Figure = Area of Square - Total Area of Unshaded Figures}\)

Answer 7

There is another way to do it. Let me post that.

Answer 8

ok

Answer 9

Find the area of all those right triangles plus the area of the rectangle. Let's number them:

Answer 10

we can do the first way xD

Answer 11

or the second

Answer 12

So we can find the area of each individual shaded figure to find the total shaded area.
\(A_t = A_1 + A_2 + A_3 + A_4 + A_5 + A_6\)

Answer 13

You know the formulas for area of a triangle and area of a rectangle correct?

Answer 14

yes

Answer 15

we can do the first one

Answer 16

Actually, it's more efficient to do the second method.

Answer 17

Okay let's do that one lol

Answer 18

Actually, I was hoping that you would be inspired to try this on your own and post your attempt here using that formula I gave you above. See if you can find the areas of each small figure and post here:
\(A_1 = ?\)
\(A_2 = ?\)
\(A_3 = ?\)
\(A_4 = ?\)
\(A_5 = ?\)
\(A_6 = ?\)

Answer 19

ok

Answer 20

the base of the number 1 triangle is 5 and the height is 2 or 3?

Answer 21

It really doesn't matter to be honest. Either of the legs of the triangles can be considered base or height. As long as you're using the formula \(A = \dfrac{bh}{2}\) to calculate the area of the triangles

Answer 22

yeah I'm using that formula

Answer 23

how do I find the base and height of a triangle?

Answer 24

You measure the lengths of the segments for both legs of a right triangle. For example for Triangle 1, Leg 1 = | 1 - (-5)| = |1 + 5| = | 6 | = 6

Answer 25

leg 2 1 -(-3) = 1+3 = 4

Answer 26

You can also just count squares as well which would be easier to do mentally

Answer 27

did i do it correct?

Answer 28

with the second leg

Answer 29

If you count the squares, you will see that the measure of Leg 2 is just 3 units.

Answer 30

oh I thought i had to your math thing lol

Answer 31

the area is 12

Answer 32

my bad I was writing

Answer 33

The "math thing" I did is called absolute value. It's just the computation used to find the length of a segment on an xy plane. In this case, the leg occurs vertically, so you would write Length of Leg 2 = |\(y_2 - y_1| = | 0 - (-3)| = | 0 + 3| = | 3 | = 3\)

Answer 34

The area is 5 for triangle number 2

Answer 35

How did you get 5 for the area of triangle 2? Mind showing the work you did to come up with that?

Answer 36

Did you calculate the length of each leg first?

Answer 37

i counted the squares that had shade on them.

Answer 38

I would recommend that you count the squares rather than use the formula

Answer 39

i cant draw rip

Answer 40

yeah that part is 5

Answer 41

I thought that side was the base cause the triangle is sideways

Answer 42

First count the vertical squares. You get 5 for that. Then count the horizontal squares. You get 2 for that

Answer 43

But yeah, it's five for the area.

Answer 44

ok lol wow

Answer 45

You're correct. So far we have:
\(A_1 = 9\)
\(A_2 = 5\)

Answer 46

A3= 3

Answer 47

A4=3

Answer 48

A5=2

Answer 49

Very good

Answer 50

RECTANLGE = 20

Answer 51

So \(A_6 = 20\) Okay, time to add them all up to get the total area.

Answer 52

So \(A_t \\= A_1 + A_2 + A_3 + A_4 + A_5 + A_6
\\= 9 + 5 + 3 + 3 + 2 + 20 \\= 14 + 6 + 22 \\= 20 + 22 \\= 42\)

Answer 53

The area of the first triangle is 9. Go back and calculate

Answer 54

oh i thought it was 12

Answer 55

Calculate it now and see what you get. Clearly the lengths of each leg are 6 and 3.

Answer 56

back my laptop wouldn't allow me to type nothing like it let me do nothing

Answer 57

10/10 grammar

Answer 58

yea it's 9

Answer 59

i put the height 4 on accident instead of 3

Answer 60

we did it!