6.G.1 Area of Parallelograms Disaster AREAS! Teachers, please look at the notes of each slide for more information about the lesson. 6.G.1 Area of Parallelograms

Why learn about AREA? Well…. we hear about areas of destruction everyday on the news!

Oklahoma tornado damage, May 1999 F5 TORNADO: INCREDIBLE  Run kid, run… The news may report how many square miles of damage was caused by a tornado. Do you see a particular shape in the picture above? A Parallelogram perhaps? Who sees the Parallelogram??

------ Detective’s ------ Tape off an area of a crime sceen to protect the evidence. Need a close-up on 24? Detectives must tape off the area of a crime scene. The exact amount of area in a crime scene could be vital information when the case goes to court!

------ Hurricane Katrina ------ August 29, 2005 Winds: 125 mph Storm Surge: 30 ft high waves Loss of life: Approximately 1,500 That’s big… 80% Flooded Hardest Hit Areas Hurricane Katrina hit the Gulf Coast on August 29, 2005. The hurricane was a category 5 at sea, but by time it hit land it was downsized to a strong category 3. Winds reached 125 miles an hour. Storm surge (how high the waves are) 30 ft in height. The hurricane produce a reported 43 tornadoes as well! Approximately 1,500 people lost their lives. New Orleans Mississippi Gulf Coast

------ Hurricane Katrina ------ August 29, 2005 Official disaster area… 90,000 square miles! Here you can see the path that the hurricane took. The official disaster zone just in the United States alone is 90,000 square miles!

Area affected: 17,709 sq miles Gallons spilled: 11 million ------ Exxon Valdez ------- Major oil spill that took place on March 23, 1989 at Prince William Sound in Alaska. Area affected: 17,709 sq miles Gallons spilled: 11 million The news may report how many square miles the oil drifted in an oil spill as in this case with the Exxon Valdez. The above map tracks where the oil drifted from March 24, 1989 to June 20, 1989. Approximate AREA of the spill covers 28,500 sq. km which is about 17,709 sq. miles. The captain of the Valdez is a sailor named Joseph Hazelwood. He was initially accused of being drunk when the oil spill happened. However, he was later cleared of that charge.

Gulf of Mexico Oil Spill! Deepwater Horizon BP Oil The Deepwater Horizon was a 9-year-old offshore drilling unit that could operate in waters up to 8,000 feet deep and drill down to 30,000 feet. At approximately 9:45 p.m. on April 20, 2010, methane gas from the well, under high pressure, shot all the way up and out of the drill column, expanded onto the platform, which created an explosion. Fire then engulfed the platform. Most of the workers escaped the rig by lifeboat, however 11 worker were never found and are to have died in the explosion. After burning for approximately 36 hours, the Deepwater Horizon sank on the morning of April 22, 2010. 2,604,000 gallons per day leaked into the waters of the Gulf for over 100 days. Area affected: 86,985 square miles! Gallons spilled: 2,604,000 gallons per day leaked into the waters of the Gulf for over 100 days. Very sad…

Today’s Lesson Today, we will learn how to find the area of a parallelogram. Students must know the formula and understand why the formula works. Section 1: What is Area? Section 2: Exploring the Formula. Decompose and Compose Parallelograms into Triangles and Rectangles to find the area. Section 3: Identifying the height of a Parallelogram.

Section 1 Section 1: What is Area? Section 2: Exploring the Formula. Decompose and Compose Parallelograms into Triangles and Rectangles to find the area. Section 3: Identifying the height of a Parallelogram.

It is the measure of the space inside of a two-dimensional figure. What is Area?   It is the measure of the space inside of a two-dimensional figure. Area is measured in something called square units (u²). To find the area of a figure, you must use specific formulas. Have students try this problem on their own. Formula: A = b x h A = 6 x 4 Area of the lid of the jewelry box = 24 square units

In 5th grade you learned to find the area of a rectangle. Try this problem! Beth is making a lid for her jewelry box with square tiles as shown below. What is the area of Beth’s jewelry box? What is the formula to find the area of a rectangle? Plug the numbers into your formula. 3) What is the area of the lid to Beth’s jewelry box in square units? Have students try this problem on their own. Formula: A = b x h or A = l x w A = 6 x 4 Area of the lid of the jewelry box = 24 square units

Section 2 Section 1: What is Area? Section 2: Exploring the formula. Decompose and compose Parallelograms into triangles and rectangles to find the area. Section 3: Identifying the height of a Parallelogram.

Explore Activity Area of a Parallelogram We already know that to find the area of a rectangle we use the formula A = b • h. Well, what if I were to tell you that you use the same formula to find the area of a parallelogram? How can that be? Rectangle A = b • h Parallelogram A = b • h Let’s Explore

Explore Activity Area of a Parallelogram Each of you will be given a parallelogram. See resource at the end of the lesson document.

Explore Activity Area of a Parallelogram Since we know how to find the area of a rectangle, how can we change the parallelogram into a rectangle? Call on students for their responses. Answer: Cut off a right triangle on one side of the parallelogram, and glue it to the other side.

Explore Activity Area of a Parallelogram Draw a dotted line, perpendicular to the base, to show the triangle you will cut. Fold your paper along this line. Check to make sure all students have drawn the dotted line in the correct place. Don’t cut yet!

Explore Activity Area of a Parallelogram Question… Could the dotted line be drawn in a different location? If so, where? Yes, the dotted line can be drawn in a different location. It could be drawn on the other side of the parallelogram as displayed here. Both lines are perpendicular to the base and form right angles.

Explore Activity Area of a Parallelogram Cut along the dotted line. Glue both parts of the parallelogram onto a piece of paper to make a rectangle. glue Why is the new shape classified as a rectangle? Because it is a quadrilateral that has four right angles!

Explore Activity Area of a Parallelogram Label the base and height of your new rectangle as follows. How do these measurements compare to the base and height of the parallelogram? Answer: They are the same. They are the same! 3 in. 7 in.

Explore Activity Area of a Parallelogram What is the area of the rectangle? A = b • h A = 7 • 3 Answer: 21 square inches

Explore Activity Area of a Parallelogram original parallelogram? Why? If the are of the rectangle is 21 square inches, what is the area of the original parallelogram? Why? A = b • h A = 7 • 3 Answer: 21 square inches Why? Both shapes have the same of space inside.

Explore Activity Area of a Parallelogram We know that the area of a rectangle is A = base × height. Through this activity we discovered that the formula of a parallelogram would be the same!

You Try Find the area of each parallelogram. Show your work by writing the formula and plugging the numbers into the formula! 1) 2) 3) You try problems should be done independently. Monitor students to ensure that they are showing their work as directed. Review answers, showing the proper way to set up and solve each problem. Answer: 24 cm² Answer: 200 m² Answer: 84 ft²

Section 3 Section 1: What is Area? Section 2: Exploring the formula. Decompose and compose Parallelograms into triangles and rectangles to find the area. Section 3: Identifying the height of a Parallelogram.

Help! I’m confused! Why is the height the vertical line (8 m) and not the slanted line (10 m)? If we look back to the rectangle we created, the base and height of both the rectangle and the original parallelogram are perpendicular to each other. Therefore, the height of a parallelogram is the perpendicular line segment drawn from the top base to the bottom base. Call on students for an answer. Then, click to reveal correct answer on the screen. Have students copy correct answer from the screen onto their student notes.

All three dotted lines are correct! Below are three images of the same parallelogram. Which dotted line shows the proper height of the parallelogram? All three dotted lines are correct! All three heights represent a line segment that is perpendicular to the base. The line is drawn from the top base to the bottom base. Call on students for an answer. Then, click to reveal correct answer on the screen. Have students copy correct answer from the screen onto their student notes.

You Try For problems 1-3 draw and label the height of each parallelogram. A parallelogram in the coordinate plane has the vertices (-3,5), (4,5), (-5,-2), and (2,-2). Graph and draw the line segments to form the parallelogram. What is the length of the base and height of the shape? 4) 1) 2) 3) You try problems should be done independently. Call on students to come to the board to show their answers. Ask if it could be drawn another way. Answers will vary on problems numbers 1 - 3. Problem number 4 comes from objective 6.G.3. Answer: The base is 7 units, height is 7 units.

Closure Area is the measure of the space inside of a 2-D figure. 1. How is area measured? 2. Describe how you can take this parallelogram and decompose a triangle and use it to compose a rectangle? 3. What is the formula for the area of a parallelogram? 4. How can you recognize the height of a parallelogram? Square Units Cut the right triangle off one end of the parallelogram and glue it to the other. Area = base • height or Area = length • width It is the perpendicular line drawn from the top base to the bottom base.

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