Polygon troubles :)?

Question

Its hard to explain but i drew a picture



if not: http://img297.imageshack.us/img297/322/anstc0.jpg

(A) Find the Perimeter

(B) Find the area insdie the polygon

Answer 1

Check the image I attached...

Here I've made the polygon into a complete rectangle. The figure in red is the added triangle. It has sides 6 and 8 and is a right triangle. If you remember your Pythagorean ratios, you should know 3-4-5 and 6-8-10. Or you can prove it using:

6² + 8² = x²
36 + 64 = 100
x² = 100
x = 10

To get the perimeter, just add up the sides:
Perimeter = 1 + 10 + 9 + 4 + 10
Perimeter = 34 units

To get the area, take the big rectangle (9 x 10) and remove the area of the triangle (1/2 b * h = 6 x 8 / 2)
Area = 9 x 10 - (6 x 8)/2
Area = 90 - 24
Area = 66 sq. units

Answer 2

A. For the perimeter you need to add up all the sides.. You're missing one side, the hypothenuse of a triangle, so you need to solve for that using the Pythagorian Therum (nevermind my spelling.)

That's a little tricky, and trickier to explain. See where the four is? You're going to have to draw a line from the top corner where the 4 is straight across parallel to the base. That's going to be the base of your triangle and it's going to be 9 (for now.)

Now where the 1 is, you're going to have to draw a line straight down from the right corner to the bottom line. Now you should have a triangle inside of that shape.

The base of that triangle is going to be 8. (You take the original base, 9, and subtract 1 because it's not going all the way to the edge of the shape.)
The side of the triangle is going to be 6. (You have to subtract 4 from 10 since you are not going to use the rectable at the bottom.)

So now you have a triangle with one side is 6, and the other is 8.

Use the a^2 x b^2 = c^2 to solve for the diagnol side.
Your answer should be 10.
(36 + 84 = 100... c^2 = 100 so c =10.)

Now add up all the sides... 1 + 10 + 9 + 4 +10 = 34

B) Now that you know all the sides, finding the area shouldn't be too bad... First find the area of the bottom rectangle, then the area of the vertical rectangle, and finally the area of the triangle you created to solve for the perimeter. (Make sure you don't count an area twice.)
You should have the formulas for computing area.


The answer should be 36 + 6 + 24 = 66.

Answer 3

The easiest way to tackle this problem is to break the image into two rectangles and a right triangle. Draw a line from the right side of the length on top (1) straight down. That will cut a small, skinny rectangle on the left that is 1x10. Now draw a line from the top of the segment that is on the extreme right (4) and go straight left back to the line you drew earlier. That rectangle would have the dimensions 4x8. Finally, you have a right traingle with left leg (6), bottom leg (8), and hypotenuse (10). I know the hypotenuse is 10 because of pythagoreans theorem (a² + b² = c² where c is the hypotenuse).

To find the perimeter, you need to add up all the sides. Since we now know the angled side is 10 long .. you simply ...

10 + 9 + 4 + 10 + 1 ... that's the perimeter ... 34

For the area, take the 2 rectangles and 1 triangle we made earlier. Find the area of each piece and add them up.

Skinny left ... 1 x 10 = 10 units² of area

Bottom Rectangle ... 4 x 8 = 32 units² of area

The triangle ... ½bh = ½(8)(6) = ½(48) = 24 units² of area

add them all together ... 10 + 32 + 24 ... 66 units²

Answer 4

to find the perimeter you must first find the missing side. using the formula a^2 + b^2 = c^2 you will find the missing side to be 10. now add all the sides.

to find the area first find the area of the complete rectangle and subtract off the missing triangle. 90 - 24 = 66

Answer 5

perimeter....
let the vertices be A,B,C,D,E where AB=1,CD=4,DE=9,EA=10
drop a vertical line from B and a horizontal line from C.now let the point of intersection of those 2 lines be F.now BFC is a right angle triangle...and BF=10-4=6.(from figure we can get this....BF=EA-DC)
similarly...CF=9-1=8
now, BC=(6^2 + 8^2)^1/2=10 (by pythagorous theorem)
now perimeter=1+10+4+9+10=34
and area=area of each small rectangle formed by extending BF n CF
if you draw a figure you can easily understand...

Answer 6

Thats a hard one for area dud, good luck

length for the angled side is 6 + 8 or less.

Sorry I couldn't help more

good luck : D