| The area of a polygon is the number of square units inside that polygon. Area is 2-dimensional like a carpet or an area rug. A triangle is a three-sided polygon. We will look at several types of triangles in this lesson. |
![[IMAGE]](http://www.mathgoodies.com/lessons/vol1/images/intro_triangle.gif) |
![[IMAGE]](http://www.mathgoodies.com/lessons/vol1/images/parallelogram_triangle.gif)  |
To find the area of a triangle, multiply the base by the height, and then divide by 2. The division by 2 comes from the fact that a parallelogram can be divided into 2 triangles. For example, in the diagram to the left, the area of each triangle is equal to one-half the area of the parallelogram. |
Since the area of a parallelogram is  , the area of a triangle must be one-half the area of a parallelogram. Thus, the formula for the area of a triangle is: |
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or |
 |
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where  is the base,  is the height and · means multiply. |
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| The base and height of a triangle must be perpendicular to each other. In each of the examples below, the base is a side of the triangle. However, depending on the triangle, the height may or may not be a side of the triangle. For example, in the right triangle in Example 2, the height is a side of the triangle since it is perpendicular to the base. In the triangles in Examples 1 and 3, the lateral sides are not perpendicular to the base, so a dotted line is drawn to represent the height. |
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| Example 1: |
Find the area of an acute triangle with a base of 15 inches and a height of 4 inches. |
![[IMAGE]](http://www.mathgoodies.com/lessons/vol1/images/acute_triangle.gif) |
| Solution: |
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 =  · (15 in) · (4 in) |
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= · (60 in2) |
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= 30 in2 |
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| Example 2: |
Find the area of a right triangle with a base of 6 centimeters and a height of 9 centimeters. |
![[IMAGE]](http://www.mathgoodies.com/lessons/vol1/images/right_triangle_6x9.gif) |
| Solution: |
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= · (6 cm) · (9 cm) |
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= · (54 cm2) |
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= 27 cm2 |
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| Example 3: |
Find the area of an obtuse triangle with a base of 5 inches and a height of 8 inches. |
![[IMAGE]](http://www.mathgoodies.com/lessons/vol1/images/obtuse_triangle.gif) |
| Solution: |
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= · (5 in) · (8 in) |
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= · (40 in2) |
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= 20 in2 |
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| Example 4: |
The area of a triangular-shaped mat is 18 square feet and the base is 3 feet. Find the height. (Note: The triangle in the illustration to the right is NOT drawn to scale.) |
![[IMAGE]](http://www.mathgoodies.com/lessons/vol1/images/rt_triangle_ex4.gif) |
| Solution: |
In this example, we are given the area of a triangle and one dimension, and we are asked to work backwards to find the other dimension. |
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18 ft2 =· (3 ft) · |
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Multiplying both sides of the equation by 2, we get: |
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36 ft2 = (3 ft) · |
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Dividing both sides of the equation by 3 ft, we get: |
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12 ft = |
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Commuting this equation, we get: |
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= 12 ft |
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| Summary: |
Given the base and the height of a triangle, we can find the area. Given the area and either the base or the height of a triangle, we can find the other dimension. The formula for area of a triangle is: |
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or |
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where is the base, is the height |
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Finding the area of a circle 
A circle’s area is found using the formula:  But where does this formula come from? Let’s find out … |
What we’re going to do is break up a circle into little pieces, and then reassemble it into a shape that we know the area formula for … the rectangle.
Maybe you’re wondering
how on earth you can rearrange pieces of a circle to make a
rectangle! Well, just watch … it’s easy!
We’ll start with the circle that we want to break up:
Now split the circle into quarters:
Then reassemble them to try to make a rectangle:
Not exactly a rectangle, is it? But we’re not done yet!
Let’s break the circle into
eighths instead:
… and arrange
these pieces into a rectangular shape:
This is certainly starting to
look like a rectangle … but we’re not there yet! The next step is to go back and try splitting the circle into
sixteenths. Here are the pieces:
This time when we put them together, they are much closer to looking like a rectangle! See what you think:
The goal is to make a shape that is as close to a rectangle as possible, so that we can find its area using the rectangle formula
A = L x W
… but this shape
does not have straight sides, so the formula wouldn’t be very accurate.
Let’s go one step further, and break up the circle into a
whole bunch of little pieces. When we rearrange all the pieces, the shape would look something like this:
This is very close to a perfect rectangle! But you can see that the top and bottom are
still not perfectly straight … they are definitely a little bumpy.
Can you visualize what would happen if we kept going? If we continued to break the circle up into tinier and tinier pieces?
Eventually, the bumps would become so small that we couldn’t see them, and the top and bottom of the shape would appear perfectly straight. This is what we would see:
A perfect rectangle! Now all we have to do is find its area, using the formula A = L x W
The next question is,
‘How long are the length and width of our rectangle made from circle parts?’
Let’s go back to an earlier picture, so you can see the circle parts more clearly:
The original circle’s outside length was the distance around, or the circumference of the circle:
Half of this distance around,
, goes on the
top of the ‘rectangle’, and the other half of the circle, also length
, goes on the
bottom 
In other words, all of the red and blue pieces add up to 
, the circumference. The sides are just the radius of each of the pieces, or the radius of the circle, r.
So we know the length is and the width is r
Now we can find the area of the shape, using the rectangle formula:
… and there we have the formula for the area of the circle we started with!Welcome back everybody. I do hope you all had a wonderful break are fully refreshed, raring too go and are ready for the final part of this semester.
Songkran - Thai New Year
The Thai New Year (Songkran) is celebrated every year on 13 April to 15 April. It is also celebrated in Laos (called pi mai lao or ‘Lao New Year’ in Lao), Cambodia, Myanmar (where it is called Thingyan), and by the Dai people in Yunnan, China. Sri Lanka also celebrates a similar festival called Sinhalese and Tamil New Year on the same dates.
The date of the festival was originally set by astrological calculation, but it is now fixed . If these days fall on a weekend, the missed days off will be taken on the days immediately following Songkran falls in the hottest time of the year in Thailand, at the end of the dry season. Until 1888 the Thai New Year was the beginning of the year in Thailand; thereafter 1 April was used until 1940. 1 January is now the beginning of the year. The traditional Thai New Year has been a national holiday since then
New year traditions the most obvious celebration of Songkran is the throwing of water. People roam the streets with containers of water or water guns, or post themselves at the side of roads with a garden hose and drench each other and passersby. This, however, was not always the main activity of this festival. Songkran was traditionally a time to visit and pay respects to elders, including family members, friends and neighbours.
Besides the throwing of water, people celebrating Songkran may also go to a wat (Buddhist monastery) to pray and give food to monks. They may also cleanse Buddha images from household shrines as well as Buddha images at monasteries by gently pouring water mixed with a Thai fragrance over them. It is believed that doing this will bring good luck and prosperity for the New Year. In many cities, such as Chiang Mai, the Buddha images from all of the city’s important monasteries are paraded through the streets so that people can toss water at them, ritually ‘bathing’ the images, as they pass by on ornately decorated floats. In northern Thailand, people may carry handfuls of sand to their neighborhood monastery in order to recompense the dirt that they have carried away on their feet during the rest of the year. The sand is then sculpted into stupa-shaped piles and decorated with colorful flags.
Some people make New Year resolutions - to refrain from bad behavior, or to do good things. Songkran is a time for cleaning and renewal. Besides washing household Buddha images, many Thais also take this opportunity to give their home a thorough cleaning.
The throwing of water originated as a way to pay respect to people, by gently pouring a small amount of lustral water on other people’s hands or over a shoulder as a sign of respect. Among young people the holiday evolved to include dousing strangers with water to relieve the heat, since April is the hottest month in Thailand (temperatures can rise to over 100?F or 40?C on some days). This has further evolved into water fights and splashing water over people riding in vehicles. 
The use of plaster is also very common having originated in the plaster used by monks to mark blessings Some children having fun at the Bangkok Zoo during Song KranNowadays, the emphasis is on fun and water-throwing rather than on the festival’s spiritual and religious aspects, which sometimes prompts complaints from traditionalists. In recent years there have been calls to moderate the festival to lessen the many alcohol-related road accidents as well as injuries attributed to extreme behavior such as water being thrown in the faces of traveling motorcyclists.
The water is meant as a symbol of washing all of the bad away and is sometimes filled with fragrant herbs.
World Maths Day 2008
In 2008, on 5 March, students from over 150 countries combined to correctly answer 182,455,169 mathematics questions. This broke the previous record of 38,904,275 correct answers.
During World Maths Day 2008 there were 5,172,844 sign ins over the 48 hour period.
The Grade Five Mathletes (our very own world record breakers)
World Maths Day (known as World Math Day in American English) is one of the world’s largest global educational events, aiming to lift numeracy standards in a fun and meaningful way. World Maths Day takes place on the first Wednesday in March. In 2009 World Maths Day will be on Wednesday 4 March.
The event is free of charge for both schools and students. Registrations are completed online at the World Maths Day website. Registrations for 2009 will commence on the site in February 2009.
About the event
Questions set come under four categories: addition, subtraction, multiplication and division. In each game, the student has one minute to answer as many of these questions of a random category as they can. The level of difficulty is age appropriate.
When playing a game, the website will attempt to find other players of the same level to match the player against. If no matches are found, the player plays “against” a computer (which answers questions at pace similar to the past history of the student). After each game, the results are shown together with the competitors’ results. The game will be automatically lost by getting three incorrect answers.
Students can play as many times as they like over the period from both home and school. Connectivity to the internet is all that is required to play.
Participating countries
Albania, Angola, Australia, Austria, Bahrain, Bangladesh, Belgium, Bermuda, Botswana, Brazil, Brunei, Cote d’Ivoire, Canada, Canary Islands, China, Colombia, Congo, Costa Rica, Croatia, Cyprus, Czech Republic, Ecuador, Egypt, El Salvador, Eritrea, Ethiopia, Finland, France, Gabon, Gambia, Germany, Ghana, Greece, Guatemala, Haiti, Honduras, Hong Kong, Hungary, India, Indonesia, Ireland, Isle of Man, Italy, Japan, Jordan, Kazakhstan, Kenya, Kuwait, Lebanon, Lesotho, Libya, Luxembourg, Malaysia, Malta, Mexico, Morocco, Mozambique, Nepal, Netherlands, New Zealand, Nigeria, Northern Mariana Islands, Norway, Oman, Pakistan, Panama, Papua New Guinea, Paraguay, Philippines, Poland, Portugal, Puerto Rico, Qatar, Republic of Korea, Romania, Russia, Saudi Arabia, Seychelles, Singapore, Slovakia, South Africa, Spain, Sri Lanka, Sudan, Sweden, Switzerland, Taiwan, Tanzania, Thailand, Turkey, Uganda, United Arab Emirates, United Kingdom, United States, Uzbekistan, Venezuela and Zimbabwe
Save the Amazon Rainforest!
What exactly is the Amazon rainforest? Who lives there? What plants and animals does it house? Did you know that this amazing ecosystem is endangered? In this webquest you are going to find out the answers to these questions and much more…..
Introduction
Do we want this?
or this?
The Amazon rainforest is an ecosystem where thousands of species of plants and animals grow. Some of them are unique to this area. It also houses groups of indigenous peoples who are finding it harder and harder to keep their traditional way of life because of the destruction of their habitat. In this webquest you are going to find out about the amazing flora and fauna of the Amazon rainforest, and about the incredible Yanomami.
And together you are going to try and find solutions to stop the destruction of this amazing biome!
TASK
You are going to form groups of 3 students.
Members of each group will:
1-Research an aspect of the Amazon rainforest.
2-Share the results of their research with their group.
3-Create a poster about their aspect of the Amazon rainforest.
4-Give a group presentation which consists of all information gathered.
5-Write a letter to the UN convincing them of the need to protect the Amazon rainforest.
This week we had our group presentations on the Amazon rainforest.
Below are some pictures of our guest experts. They included biologists, zoologists and anthropologists.
Make a Weather Station Overview:
Meteorology is the study of all changes in the atmosphere, i.e. the layers of gases (air) that surround the earth. In order to do this we will need to study current weather conditions and the general climate in your area, and identify which factors most affect your daily temperature.
To do this, you must first make a weather station. Begin by designing and building some of the same instruments that meteorologists use.
Materials:
Instructions:
You will work in small groups to design and construct weather instruments. All of the instruments will then be put together to create a class weather station. By collecting your own data, you will learn more about weather through a process similar to the one that professional meteorologists use.
Part 1: Introduction
- Make a Weather Learning Log: This log will be an important tool. You will use it to record weather information as time goes on.
- Write your name on the notebook (if you are working as a group, each member should put their name on it). As an optional activity, you can decorate the cover as well.
- Discuss and answer the following questions. Record your answers in your Journal.
- What do you think of when you hear the word “weather”?
- How does weather affect our daily lives? (Ex. what kinds of clothes do you wear, outdoor activities that you do, etc.)
- What kinds of things would you look for if you wanted to describe the weather of a particular day to someone else?
- What kinds of information are important to collect?
- Brainstorm designs for instruments that you could use to measure each of the following AND answer the corresponding questions in your Journal:
- Temperature: What does temperature have to do with weather?
- Wind: How can you describe wind? Are there different types of wind? Can you measure how fast the wind is blowing and where its blowing to?
- Precipitation: Are there different types of precipitation?; How could rain be measured?
- Air pressure: What is air pressure? Why should we measure it? What does air pressure have to do with weather?
- Sky conditions: Write a list of standardized terms to describe sky conditions (e.g. clear, partly cloudy, overcast with openings, overcast, etc.)
- Present: Each group should first design the class weather instruments.
- Additionally, the class should develop a list of standardized sky condition terms to use for the rest of this project.
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Part 2: Make a Class Weather Station
- Practice with the Instruments: repeatedly test the instruments for accuracy.
- Record your measurements: Please follow the guidelines below.
NOTE: If you are combining Activities 1 and 2, record your measurements in the column marked “Class Instruments” in the Current Conditions table.
- Temperature (Use a commercial outdoor thermometer and record in degrees Celsius):
- Sky conditions (Observe outside and use one of the standardized sky condition terms. For example, clear, partly cloudy, overcast with openings, overcast, etc.):
- Wind (calm, light, etc.):
- Wind Direction (N, NW, W, SW, etc.):
- Wind Speed (how many times the anemometer spun):
- Precipitation Type (at data collection time - rain, drizzle, snow, none, etc.):
- Precipitation Amount (in last 24 hours. Record your findings in mm):
- Air Pressure (record your finding in the units marked on your class barometer):
World Math Day Challenge
In World Math Day Challenge (held on March 5), students from across the globe will be uniting online to play each other in real time mental arithmetic games. These are tailored to the students’ levels so students of various ages can participate.
They are expecting more than 1 million students from over 100 countries! It is one of the world’s largest participation events.
World Math Day is free of charge for both schools and students. All you need is Internet access. And, there are even prizes!
More information may be found at www.WorldMathDay.com.
Grade five are already registered and have their user names and passwords in their maths notebooks and their assignment books.
So this week lets break a world record together!
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