Today’s lesson was on the area of a regular polygon. This can be very tricky. There are some notes (link here) and in groups we worked on finding the area of some polygons. We will continue this during our next meeting. There was an in-class assignment (#55) as well as a homework assignment: #56 (download) on interior and exterior angles of a regular polygon.
I was out AGAIN for the odd classes due to illness, but again, the show must go on.
Coming up:
- BM 38 on Area of a Polygon and retakes 34-37 on Monday, 3/12
day on 3/14
Posting for points question:
Describe the steps for finding the area of a regular polygon given a side length. Be specific!
March 6, 2007 at 5:09 pm
I will do the best I can, because I am having a little trouble with this. Say that you are given a Heptagon with side length of 15in, now you must find the area. First use
(n-2) x 180 so (7-2) x 180 = 5 x 180 = 900/7 = 128.5/2 =
64.25 now use h = tan 64.25 = h/7.5 = 7.5 tan 64.25 = h
Then A= 1/2 (15)(7.5 tan 64.25) = 116.6 x 7 = 816.2
March 6, 2007 at 6:27 pm
Ryan, good work. Actually, more work than was needed. All I want is the steps- in words. I think everyone will be having some trouble with for a few days.
March 6, 2007 at 6:56 pm
1) find the angle of the triangle:
sum of triangle divided by # of sides divided by 2 = angle
2)find the hight of the triangle using the tangent of the angle
3)area = 1/2 times the length of the side times, the tangent for the hieght
March 6, 2007 at 7:00 pm
Fine the area of a regular hexagon eith side lengths of 36in
Steps…..To find the area os a regular polygon
1.)(n-2)*180=(6-2)*180=(4)180=720/6=120/2=60
2.)tan 60=h/18=18 tan 60=31.17
3.)1/2(20)(31.17)=311.7
4.)311.7*6=1870.2in
March 6, 2007 at 7:13 pm
READ THIS———-
I don’t want an example. Just the steps. There should be 4 steps.
March 6, 2007 at 7:34 pm
First you divide the polygon into equal triangles. Then you find the area of one triangle by using trigonometry. There must be a side length to find this out. Basically you are trying to find the height of the triangle when using trig. Then once you find the area of the triangle, you times the answer by how many sides there are.
March 6, 2007 at 7:38 pm
i had trouble working on some of the problems but i tryed find the area of a hexagon with lengths of 10 in
1. (n-2)180=(6-2)180=4(180)=720/6=120/2=60
use 60 to h=tan(60)(half 10)= 5 tan60 then a=.5 (10) (5tan60)=43.30(6)=259.81
March 6, 2007 at 8:55 pm
Divide polygons into equal triangles.
Find area of one triangle.
x:(8-2)180= 1080
6 x 180=1080/8=135/2=67.5 degrees
tan67.5=h/10
10tan67.5=h
the area of a triangle is 1/2(20)(10tan67.5degrees)=241.4
polygon area: 241.4(8)=1931.37 inches squared.
March 6, 2007 at 10:16 pm
Gosh, these look like examples. I don’t want examples.
I WANT WORDS!!!! THERE SHOULD BE VERY FEW NUMBERS IN YOUR POST!!!
March 6, 2007 at 10:27 pm
1. Divide Polygons into congruent Triangles
2. Find the area of 1 triangle
–Use trig. to find height
–Angle is 1/2 of an Int. Angle.
3. A poly.= A Triangle x’s # of sides
Is that enough??
March 7, 2007 at 3:33 pm
1. Divide the polygon into triangles.
2. Find the area of one triangle
- use trig to find the height
3. The angle of a polygon = area of a triangle X # of sides
This was easy for me to understand and to solve the problems.
March 7, 2007 at 3:52 pm
you have to first divide the polygon into triagles
then you solve for the hight using tangent
then you solve for the area of one triangle(1/2 bh)
then you multiply by how many triagles there are in the polygon
March 7, 2007 at 3:56 pm
1. Divide the polygon into triangles.
2. Find the interior sum of the triangle and divide it by two. That should give you the angle measurement you need for the trig. function.
3. Plug in the angle measurement to the Tangent trig. Keep it as is. Don’t solve the trig. equation.
4. To find the area of 1 triangle you use the equation: 1/2(side length)(Tan equation). The answer of this equation will be multiplied by the number of sides the polygon has.
March 7, 2007 at 4:05 pm
I thought today’s lesson was fairly easy. The steps for finding the area of a regular polygon are:
1. Divide the polygon into congruent triangles
– Use trig. to find the height
March 7, 2007 at 4:11 pm
***SOrry i messed up on the first comment accidently pushed submit, my bad =]***
I thought today’s lesson was fairly easy. The steps for finding the area of a regular polygon are:
1. Divide the polygon into congruent triangles
2. Find the are of the triangle
- Use trig. to find the height
- Angle is 1/2 of the interior angle
3. Then you find the area of the triangle by multiplying
1/2(# of side length) (1/2 of side length Tangent of x)
4. Finally you multiply that number by the n-gon and then you come out with your final answer.
Really easy stuff =]
March 7, 2007 at 4:48 pm
To find the area of a regular polygon:
1: do number of sides – 2
2:you do number of triangles * 180
3:interior angle sum divided by number of sides
4:the exterior angle is = to 360
5:360 divided by number of sides
and that how u would find the area of a regular polygon.
March 7, 2007 at 9:20 pm
1. divide Polygons into congruent Triangles
2. then find the area of 1 triangle
1) Use trig. to find height
2)Angle is 1/2 of an Int. Angle.
3. then you multiply 1/2(# of side lengths)(1/2 of side length and tangent of x)
4. then you multiply the answer by the #of sides.
March 7, 2007 at 9:45 pm
1. Divide the polygon into triangles
2. Solve for the hight using tangent and the angle you solved for
3. Solve for the area of one triangle .5 base x Height
4. Multply by the number of sides
March 8, 2007 at 1:18 pm
1) divide the polygon into the triangles it consists of.
2) find the height and base of one triangle
3) plus in cos, tan, or sin depending on what your trying to find
4) multiply base times height
5)multiply the answer by the number of sides
March 8, 2007 at 6:50 pm
1. divide the polygon into congruent triangles.
2. Find the area of a triangle
– use trig to find the height
– angle is 1/2 of 1 interior angle
3. A polygon= A triangles # of sides.
4. then multiply the answer by the number of sides
March 8, 2007 at 8:01 pm
to find the area your given the length of each side so you use the interior angle formula to find the degree of one angle divide that by 2 and use calculus to find the last side and then you can find the area of one triangle then times it by the # of angles and you find the area…
March 8, 2007 at 8:06 pm
To find the area of a regular polygon:
1) Divide the Polygons into congruent triangles
2) Find the sum interior of a regular polygon
3) Divide the sum interior angle by the sides of the given polygon to get 1 angle
4) Divide your answer by 2 to get the angle in the triangle
5) Find the area of 1 triangle
– use trig to find the height (tangent of angle)
– Angle is 1/2 of 1 interior angle
6) Area of poly = (area of triangle) x (# of sides)
***leave answer to area of triangle in calculator then round the final answer***
March 9, 2007 at 8:53 am
1.) Divide the polygon into a triangle.
2.) Find the height of the triangle. Divide the perimeter by # of sides in the polygon if given.
3.)Find the sum of the interior angle.
4.) Divide the sum of the interior angle byt he # of sides.
5.) Divide that answer by 2.
6.) Use trig to find the height. Use the formula 1/2b(h)angleTAN(x)
7.)Multiply that answer by 2.
March 12, 2007 at 7:04 pm
Step 1: Divide Polygons into congruent Triangles
Step 2: Find the area of 1 triangle
-Use trig to find height
-Angle is .5 of an int. angle.
Step 3: Multiply 1/2(# of side lengths)(1/2 of side length and tangent of x)
Step4: Multiply the answer by the #of sides.
March 12, 2007 at 7:28 pm
I actually understanded todays lesson fairly well, from what i though.
the steps to find the area of a pentagon are:
1)Divide the polygon into CONGRUENT triangles.
2)Find area of ONE triangle.
You are give the base, so you need to find the height by using trig. then you find the area of a triangle by doing 1/2bh.
3)You then multiply 1/2 the # of side lenth times 1/2 o the side lengths and the TAN of x.
4) Multiply that answer by the number of sides in the polygon.
Then you have your answer and you put it to UNITS SQUARED. =]
March 12, 2007 at 7:48 pm
1. Divide the polygon into triangles
2. Find the are of the triangle
*Use trig. to find the height
*Angle is 1/2 of the interior angle
3. Multiply 1/2(# of side lengths)(1/2 of side length and tangent of x)
4. Then mulitply the answer by the # of sides