Question

I need help

Answer 1

Question

Answer 2

Number 32 does seem to have 4 triangles

Answer 3

i drew the lines inside to count

Answer 4

@jim_thompson5910 help me plz

Answer 5

Do you know the area of a triangle?

Answer 6

i try to do them but i kept getting 6 for the area for number 32

Answer 7

notice you have 2 triangles

the first triangle is in quadrant 1
the second triangle is in quadrant 4

Answer 8

yes

Answer 9

both triangles have a base of 6, and a height of 3

Answer 10

how u get base of 6 and height of 3 it doesnt tell u

Answer 11

count out the number of square units along the base

ie count the number of spaces between Q and S

Answer 12

each tick on the grid represents 1

Answer 13

okay i see it

Answer 14

wat next?

Answer 15

use the formula

A = (b*h)/2

A = area of triangle
b = base
h = height

Answer 16

9

Answer 17

that's the area of ONE triangle, but there are 2 of them

both triangles are congruent (one is a mirror image of the other)

Answer 18

oh oh 18

Answer 19

yep the quadrilateral (in this specific case, a kite) has area 18 square units

Answer 20

for #32

Answer 21

hb number 33?

Answer 22

it slooks harder since its on a angle

Answer 23

what's the distance from T to S?

Answer 24

3

Answer 25

so that's the base

Answer 26

height is 3 right?

Answer 27

too

Answer 28

if you started point R, and you went straight down, how many units do you count?

keep going til you hit the x axis

Answer 29

5

Answer 30

that's the height

Answer 31

b = 3
h = 5

Answer 32

use the same formula to find the area of the triange

Answer 33

triangle*

Answer 34

7.5

Answer 35

yes, there are 2 of these triangles so the total area is 15

Answer 36

oh

Answer 37

number 34?

Answer 38

are you able to determine the coordinates of Q, R, S, or T?

Answer 39

yes

Answer 40

tell me what they are

Answer 41

q=-3,-2
r=-2,2
s=2,3
t=1,-1

Answer 42

don't forget parenthesis around each ordered pair

but you have the correct coordinates

Answer 43

okay

Answer 44

what do i do with coor?

Answer 45

Q is (-3,-2) and the opposite point S is (2,3)

what is the distance from Q to S?

to find out, use the distance formula

\[\Large d = \sqrt{(x_1-x_2)^2+(y_1-y_2)^2}\]

Answer 46

2

Answer 47

the distance is base right?

Answer 48

Q = (-3,-2)
\[\Large Q = ({\color{red}{-3}},{\color{blue}{-2}}) = ({\color{red}{x_1}},{\color{blue}{y_1}})\]
S = (2,3)
\[\Large S = ({\color{green}{2}},{\color{purple}{3}}) = ({\color{green}{x_2}},{\color{purple}{y_2}})\]



\[\Large d = \sqrt{(x_1-x_2)^2+(y_1-y_2)^2}\]
\[\Large d = \sqrt{({\color{red}{x_1}}-{\color{green}{x_2}})^2+({\color{blue}{y_1}}-{\color{purple}{y_2}})^2}\]
\[\Large d = \sqrt{({\color{red}{-3}}-{\color{green}{2}})^2+({\color{blue}{-2}}-{\color{purple}{3}})^2}\]
I'll let you finish up

Answer 49

20

Answer 50

no

Answer 51

what is `-3-2` equal to?

Answer 52

-5

Answer 53

sqrt2 equal 10?

Answer 54

no no my bad25

Answer 55

So we have...
\[\Large d = \sqrt{({\color{black}{-3}}-{\color{black}{2}})^2+({\color{black}{-2}}-{\color{black}{3}})^2}\]
\[\Large d = \sqrt{(-5)^2+(-5)^2}\]
\[\Large d = \sqrt{25+25}\]
\[\Large d = \sqrt{50}\]
the exact distance from Q to S is \(\Large \sqrt{50}\) units. The approximate distance is \(\Large \sqrt{50} \approx 7.0710678\) (use a calculator with a square root function)

Answer 56

that is base right?

Answer 57

no, but it will help us find the area

Answer 58

what is the distance from R to T ?

Answer 59

can i use the diatance formula for the 32 and 33 too?

Answer 60

you could but it's faster to do what we did beforehand

Answer 61

why cant we do 34 like the other problems?

Answer 62

we could use the distance formula to find out the distance from Q to S in #32

but since Q and S lie along the same horizontal line, it's much faster to count out the spaces between the two

OR you could subtract the x coordinates

Answer 63

#34 is different because none of the sides are completely vertical or horizontal

Answer 64

and it's not easy to split up the figure into triangles that have one side that is completely vertical or horizontal

Answer 65

oh

Answer 66

18

Answer 67

I think you meant \(\Large \sqrt{18}\) right?

Answer 68

yes

Answer 69

4.24

Answer 70

The exact distance from R to T is \(\Large \sqrt{18}\). Correct

Answer 71

yes

Answer 72

why did we bother with all this? because we can use these diagonal lengths to find the area

formula

area of kite = (p*q)/2

p = length of one diagonal
q = length of other diagonal

Answer 73

In this case, the length of one diagonal is sqrt(50) while the other length is sqrt(18)

Answer 74

oh

Answer 75

450

Answer 76

\[\Large A = \frac{p*q}{2}\]
\[\Large A = \frac{\sqrt{50}*\sqrt{18}}{2}\]
\[\Large A = \frac{\sqrt{50*18}}{2}\]
\[\Large A = \frac{\sqrt{900}}{2}\]
\[\Large A = \frac{30}{2}\]
\[\Large A = 15\]


the area of the entire figure is 15 square units

Answer 77

oh

Answer 78

thank you

Answer 79

no problem

Answer 80

i think i understand how to do it