Another sample problem for Meet 4

Given a square with an equilateral triangle removed. If the square has a side of 6cm, what is the area of the figure, exactly?

(The phrase "exactly" means if we get a square root, we won't approximate it with a decimal, we'll just leave it, which is probably what they'll do on the real test, since calculators aren't allowed.)
We've got a 6x6 square with a triangle cut out. Let T= Area of the Triangle. Area of figure = 36-T. There are 3 ways to solve the triangle - A)Pythagorus, B)Heron, or C) memorize that equiateral triangle. If memorized, side of 1 means height of ½√3, a side of 6 means a height of 3√3 so the area is ½ bh = ½ x 6 x 3√3 = 9√3
Or use Heron √(s(s-a)(s-b)(s-c)) where s = semi-perimeter = 9 T =√(9(9-6)(9-6)(9-6))
T=√(9*3*3*3)=3*3√3 =9√3
So A = 36-9√3

Solving the sample problem

A glass prism is an equilateral triangle on one end and is 6 inches long. The perimeter of the triangle is 3 inches. What is the total surface are of the prism, exactly?

Well, let's see... we have a triangle with perimeter of 3", so each side of the triangle must be one inch. We are trying to figure out the total surface area which includes 3 large rectangles and 2 small triangles (on at each end).
The rectangles area easy 6"x 1" = 6 sq. inch per rectangle times 3 rectangles is 18 sq. in.
The triangles have a base of one and a height of ... hm. Draw the red line shown in the diagram. We now have a right triangle with legs of 1/2 and h, and a hypotenuse of 1. Turn to Pythagorus for help: a² + b² = c² .
(½)² + h²= 1²

¼+ h²= 1

h²= ¾ (Now take the square root of both sides which means taking the square root of both the numerator and denominator on the right hand side to get ...

So our total area is 18 plus 2 * 1/2 bh Hence 18 + bh, or 18 +( 1) √3 / 2

sq in

Scores and Team Assignments for Meet 4

Look's like we all could use another practice session or two. For more practice, go to
the link at right and find "past meet papers" for Meet 4.

Next Monday is Meet 4 at SPA. You'll need to get out of class early to board the bust to SPA. Get your pass from the office on Monday.

Here's how I decide who will be on the teams:
Your total is the total of 3 numbers 1) Last Meet's score, 2) All other meet scores averaged, and 3) You practice scores for this meet. If you are absent for a meet or practice, I take the average scores of the 3 or so scores above and below you and subtract 2 points and use that number instead of a zero. However if you missed both practices, I will leave the second set at zero.

HERITAGE

Name	Mt1	Mt2	Mt3	P4a	P4b	P4c	P4d	Total
Allison Rocke	16	28	21	3	3			44.5
Nick Bachman	12	28	16	4	8	12	6	43.5
Joe Dill	16	14	21	6	4	10	10	43.5
Gabriel Fromm	8	18	12	6	4	10	4	31.0
Julia Michienzi	8	12	10	0	2	0	6	22.0
Aidan McNally	8	10	10	0	0	0	0	19.0
Angela Gotham		8	14	0	0		2	18.5
Aiden Jacobs	0	12	8	4	0	0	0	15.0
Amanda Keiser	0	6	10	4	2	0		14.5
Simon Meyer	2	10	8			0	0	14.0
Hannah Skarstad	0	4	6	2	2	4	0	10.0
Gabriel Rivera	2	6	4			0	0	8.0
Jonathan Search		6	2					5.0
Anna Barton	4	0				2	0	2.5
Ben Archambeau		4				0	0	2.0

FRIENDLY HILLS

Name Monte Fischer	Mt1 20	Mt2 28	Mt3 20	P1 4	P2 14	P3 14	P4 5	Total 53.3
Elizabeth Whitcomb	12	8	16	8	8	12	2	33.5
Matthew Morse	8	16	14	4		8	6	30.5
Alex Nilles	14	8	16	2		4	4	29.5
Thomas Miranda	8	16	16	0		4	2	29.5
Vic Fischer	8	20	9	0	14	8	2	29.0
Frank Sullivan	10	12	16	2		2	1	28.3
Matt Richards	14	8	10	4		10	6	26.0
Carter Henry	4	10	12	2	8	6	0	23.0
Brigham Williams	6	8	11	0	6	2	0	20.0
Greta Prokosch		12	5	4	8	4	4	16.0
Tobiah Markovitz	8	0	10	2		1	0	14.8
Allie Prokosch		9	4	0	10	2	0	11.5
Daniel O'Reilly		12	2	0		4	4	10.0
Nathan Whitcomb	4	6	4	0	4	0	0	10.0
Dev Bhakta		6	5	0		0	1	8.3
Kieran White	4	4	2	0	2	2	0	7.0
Lendale Smith	4	0	2	0				4.0
Logan Woods	4	2		0		1	2	3.8
Mandi Wen	0	6						3.0
Luc Kaderlik	2	4						3.0
Laura Skemp	0	4		0		0	0	2.0
Danielle Stiel	0	0	2	0		0	0	2.0
Jack Korte		0	0	2				0.5
Charlie Rutman	0	0						0.0
Hannah Kirby	0	0	0	0		0	0	0.0
Maureen Anderson		0	0			0	0	0.0

Meet 4 practice results.

Difficult material for meet 4. Make sure not to miss practice next week.
Here are the scores from today. Many of you got zero this morning. Below are the ones who managed to get one or more correct.

Here's an easy formula for the area of a triangle if you know 3 sides.
s=1/2 permimeter A=sqrt(s(s-a)(s-b)(s-c)
Example: Let's use our 3"-4"-5" triangle
s =1/2 of (3+4+5) so s is 6
A = sqrt( 6(6-3)(6-4)(6-5) )
A= sqrt(6*3*2*1)
A=sqrt(36)
A=6
A=6 sq.in.
Example 2: As in today's problem an equilateral triangle with perimeter 18
a, b, and c, are 6. s=9
A = sqrt( 9*(9-6)*(9-6)*(9-6) ) = sqrt (9*3*3*3) = 3*3*sqrt(3)=9*sqrt(3)

Heritage

Allison Rocke			43.0
Nick Bachman	4	8	39.0
Joe Dill	6	4	38.5
Gabriel Fromm	6	4	27.5
Julia Michienzi	0	2	20.5
Aidan McNally	0	0	19.0
Angela Gotham	0	0	18.0
Aiden Jacobs	4	0	15.0
Amanda Keiser	4	2	14.5
Simon Meyer			14.0
Hannah Skarstad	2	2	9.0
Gabriel Rivera			8.0
Jonathan Search			5.0
Ben Archambeau			2.0
Anna Barton			2.0

Friendly Hills

Elizabeth Whitcomb	8
Monte Fischer	4
Matthew Morse	4
Matt Richards	4
Greta Prokosch	4
Frank Sullivan	2
Alex Nilles	2
Carter Henry	2
Tobiah Markovitz	2
Jack Korte	2

Top Individuals in the SE Metro Region

Remember, top 10 at the end of the year get medals, top 3 from each school get ribbons.

Can Joe Dill catch the top 10?
Can Thomas Miranda close the gap?
Can Nick Bachman hold on in the top 10?
Can Monte Fischer catch Milo for the #1 spot?
Will Frank Sullivan end up as the top 5th grader? (Sorry Frank, no medal for that.)
Can Allison catch Michelle and be the top girl in the division?

1	Milo	Wittenberg	m	8	SPA	26	26	22	74
2	Monte	Fischer	m	8	Friendly	20	28	20	68
3	Michelle	Heilig	f	8	SPA	22	24	22	68
4	Thomas	Mellen	m	8	South	22	22	22	66
5	Joe	Bricher	m	8	Trinity	18	28	20	66
6	Allison	Rocke	f	8	Heritage	16	28	21	65
7	Ben	Konstan	m	6	SPA	18	28	16	62
8	Kelton	Holsen	m	8	South	18	28	15	61
9	Netta	Kaplan	f	8	SPA	22	22	15	59
10	Nick	Bachman	m	8	Heritage	12	28	16	56
11	Patrick	Commers	m	8	SPA	20	18	18	56
12	Maeve	Mellen	f	7	South	16	20	18	54
13	Boraan	Abdulkarim	f	8	SPA	12	22	17	51
14	Navodhya	Samarakoon	f	8	SPA	22	18	10	50
15	Ruth	Olson	f	8	Trinity	12	14	16	42
16	Thomas	Miranda	m	6	Friendly	8	16	16	40
17	Michael	Hall	m	6	SPA	10	18	12	40
18	Jane	Hulse	f	8	Trinity	18	6	15	39
19	Frank	Sullivan	m	5	Friendly	10	12	16	38
20	Matthew	Morse	m	7	Friendly	8	16	14	38
21	Gabriel	Fromm	m	6	Heritage	8	18	12	38
22	Kishan	Bhakta	m	7	South	10	16	12	38
23	Eesha	Ifranullah	f	8	SPA	10	28		38
24	Vic	Fischer	m	5	Friendly	8	20	9	37
25	Joe	Dill	m	7	Heritage	16	21		37

Heritage Topples St. Paul Academy!

Heritage beat previously unbeaten SPA Gold by 1 point for a first place finish!
They passed South St. Paul and also gained a ground on second place SPA Blue.
Heritage now trails SPA Blue by only 6 points.

Although Friendly Hills Gold lost some ground on So. St. Paul, they are only 10 points out of getting a team trophy. (Remember - trophies to the top three schools.)

These scores are all unofficial. I'm missing some individual scores also.

StPaul Ac Gold 117 403
StPaul Ac Blue 106 352
Heritage Gold..118 346
So.St.Paul..... 93 323
Fr. Hills Gold. 89 313
Trinity........ 87 251
Fr. Hills Red.. 67 199
St Thomas Ac... 64 178
Heritage Red... 50 110

INDIVIDUAL SCORES
HERITAGE
Allison 10 11 21
Nick ... 8. 8 16
Joe ....14. 7 21
Gabe.... 6. 6 12
Julia....8. 2 10
Aidan....4. 6.10
Aiden... 2. 6..8
Simon... 2. 6. 8
Angela..10. 4 14
Gabriel..2. 2. 4
Amanda K.6. 4.10
Jonathan 2. 2. 4
Hannah...2. 4. 6
Anna.... ?. ?

FRIENDLY HILLS
Monte.....12 8 18
Vic........3 6 9
Matthew....8 6 14
Thomas....10 6 16
Elizabeth 10 6 16
Matt.......8 2 10
Frank.....10 6 16
Alex.......8 8 16
Carter.....4 8 12
Brigham....5 6 11
Allie......2 2 4
Nathan.....4 0 4
Dev........3 2 5
Tobiah.....4 6 10
Kieran.....2 0 2
Maureen....?
Lendale....? 2
Hannah.....0 0 0
Danielle...2 0 2

Meet 3 (at STA) Instructions & Team Assigments

HERITAGE
Next week is a meet against St. Thomas. On Monday, go to Ms. Caniff to get a pass to get dismissed early from your last hour class. At 2:50, excuse yourself from your class. Gather by the pool exit in front. I'll be there at 3:00 to get you on the bus. We'll return at 5:25 to HMS where your parents can pick you up.

Allison Rocke	8	14	43.5
Nick Bachman	4	6	38.5
Joe Dill	14	10	29.0
Gabriel Fromm	6	6	26.5
Julia Michienzi	0	4	18.0
Aidan McNally	2	4	16.5
Aiden Jacobs	2	0	14.0
Simon Meyer	0	6	13.5
Angela Gotham			8.5
Gabriel Rivera	0	2	7.5
Amanda Keiser	2	4	7.5
Jonathan Search	0	0	6.0
Hannah Skarstad	2	0	5.5
Ben Archambeau	2	4	5.5
Anna Barton			2.0

On the Team Test: Team Billy Bob 24, Team Pacman 12

FRIENDLY HILLS
Next week is a meet, so no practice in the morning. Instead, gather at the back of the school where the buses pull up. I'll be getting off the bus at about 3:20 to pick you up. We'll return at about 5:10 to FHMS where your parents can pick you up.

Monte Fischer	14	6	49.3
Vic Fischer	8	8	31.3
Matthew Morse	6	4	26.7
Thomas Miranda	4	8	26.0
Elizabeth Whitcomb	6	6	22.0
Matt Richards	6	4	21.7
Greta Prokosch	10	6	21.3
Frank Sullivan	4	4	19.7
Alex Nilles		4	17.7
Daniel O'Reilly	6	4	16.7
Carter Henry	2	4	15.3
Brigham Williams	2	4	15.0
Allie Prokosch	4	2	12.7
Nathan Whitcomb	2	6	12.0
Dev Bhakta	2	4	9.3
Tobiah Markovitz	6	4	7.3
Jack Korte	6	4	6.7
Kieran White	0	0	6.0
Mandi Wen			6.0
Logan Woods	2	4	6.0
Laura Skemp	0	0	5.3
Luc Kaderlik			5.0
Maureen Anderson		4	2.7
Lendale Smith	0	0	2.0
Hannah Kirby			1.3
Danielle Stiel	0	0	0.0