idyllic

let's draw a rectangle around the shape.

the area of the hexagon would be the area of the rectangle minus the areas of the small right triangles.

let's solve for the area of the rectangle first. this would just be 9.28 * 8 = 74.24.

now, let's do the area of the triangles. i believe the base of one triangle would be \(\frac{9.28-5}{2} = \frac{4.28}2 = 2.14\), and the height would just be 8/2 = 4.

to find the area of one triangle, we do \(\frac{2.14 \cdot 4}2\) = \(\frac{8.56}2\) = \(4.28\).

so the area of four of these triangles would be 4.28 * 4 = 17.12.

now we can solve the area of the hexagon - 

74.24 - 17.12 = 57.12.

hope this helped! please let me know if you are confused about anything i did :)

angles that are supplementary add up to 180 degrees.

so you'll need to try adding up a few angles and summing then up to see which pair adds up to 180. you can also eliminate a few pairs by just seeing which ones couldn't add up to 180 (for example, 67 and 23).

113 + 67 = 180, so the answer is angle K and angle M.

hope this helped! please let me know if you are confused about anything i did 

by vertical angles (i think that's what it is), angle 1 is congruent to angle 2, so angle 2 would also just be 50 degrees.

without vertical angles, we can see that angle 1 shares a straight angle with angle 3, so angle 3 would be 180 - 50 = 130 degrees. then we can also see that angle 3 shares a straight angle (180 degrees) with angle 2, so angle 2 would be 180 - 130 = 50 degrees. 

hope this helped! please let me know if you are confused about anything i did :)

happy belated anniversary, CPhill !!! i'm still quite an on-and-off member here, but your work is really great ! 

thanks for everything you have done!

this is a hexagon (six sides). so the sum of all the interior angles would be \((6-2)*180 = 720\).

since all of the angles given are on straight angles, we can just subtract that angle measure from 180, to get the interior angle measure.

180 - 95 = 85

180 - 62 = 118

180 - 47 = 133

180 - 45 = 135

180 - 33 = 147

now let's sum all of these together. 

85 + 118 + 133 + 132 + 147 = 615

to find the missing angle measure, let's subtract 615 from 720 (the total sum of all the interior angles). 

720 - 615 = 105.

so now we know 180 - (2x + 4) = 105.

180 - 2x - 4 = 105

176 - 2x = 105

-2x = -71

x = 71/2 = 35.5

hope this helped! please let me know if you are confused about anything i did 

i'm not sure if i should take this seriously, but...

7 * 7 = 49.

a good way to envision this is to draw 7 groups of 7, or x groups of y (whichever numbers you're multiplying).

o o o o o o o

o o o o o o o

o o o o o o o

o o o o o o o

o o o o o o o

o o o o o o o

o o o o o o o

now, you can count these, i guess, though it may be tedious.

this site also helps teach you more about basic multiplication, feel free to check it out:

https://www.ducksters.com/kidsmath/multiplication_basics.php

in a way, multiplication is very similar to addition. i'd recommend you to try and memorize the basic multiplication tables. you'll quickly notice a pattern with most of them. 

hope this helped! feel free to ask any further questions you may have.

thank you! :)

let's define two variables: l and w, to represent the length and width of this rectangle. 

we'll have a system of equations.

l = 7 + 5w

w * l = 6

now let's use substitution.

(7 + 5w) * w = 6

5w^2 + 7w = 6

5w^2 + 7w - 6 = 0

now let's solve the quadratic by using the quadratic formula.

\(x = {-7 \pm \sqrt{7^2-4 \cdot 5 \cdot -6} \over 2 \cdot 5} \)

\(x = \frac{-7 \pm \sqrt{49 + 120}}{10}\) 

\(x = \frac{-7 \pm \sqrt{169}}{10}\)(oops, i meant to do w, not x for the variable in these three; sorry about that!)

\(w = \frac{-7 + 30}{10}, \frac{-7-30}{10}\)

\(w = \frac{23}{10}, \frac{-37}{10}\)

i doubt that the width can be negative, so i believe your answer is 23/10.

hope this helped! please let me know if you are confused about anything i did 

i'm pretty sure that angle ROS is 2 times angle RTS (correct me if i am wrong).

so, we can craft an equation that looks like this:

16x - 4 = 2(7x + 5)

16x - 4 = 14x + 10

2x = 14

x = 7

now we plug x back into our expression for angle RTS.

7(7) + 5 = 49 + 5 = 54 

hope this helped! if you are confused on how i did anything, please let me know! :)

well, think of the ratio like a fraction.

4/5 = x/20

we multiply 5 by 4 to get to 20, so we must also multiply the numerator (in this case, 4) by 4, to get the amount of books Exel had.

so, Exel had 16 books, and Anne had 20 books.

hope this helped! sorry if my explanations weren't too clear. if you have any further questions, don't hesitate to ask!