copyright©amberpasillas2010 Good morning!! Thank you for taking the opportunity to improve your grade!!! Please follow these directions: 1.Take a seat and QUIETLY review your quiz. 2.AFTER we have discussed your quiz please sign the sheet in the correct class period and you are free to go. It’s that easy!

copyright©amberpasillas2010 Standards: CCSS.6.G.1: Find the area of right triangles, and special quadrilaterals by composing into rectangles or decomposing into triangles and other shapes. Essential Question: How is the formula for the area of a triangle related to the formula for the area of a parallelogram? You need your Journal, a pencil, a metric ruler and glue.

copyright©amberpasillas2010 Prepare to check your own work from Monday. 5. Use the formulas to find the area and perimeter of figure a in problem 3 if s = 5 cm. A = lwor A = bhP = 2(l + w) 6. Use the formulas find the area and perimeter of figure b in problem 3 if w = 2.5 meters. A = lwor A = bhP = 2(l + w)

copyright©amberpasillas2010 Prepare to check your own work from Monday. P = 2(l + w)

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Today we are going to learn the Area of a Triangle & Parallelogram. Then we are going to discover the Area of a Trapezoid.

Given the formula for area of a rectangle, we are going to use that information to discover the formula for the area of a triangle. Watch carefully not to miss it!

Given a right triangle Make a similar triangle,

Given a right triangle Make a similar triangle, flip it and put both triangles next to each other. What polygon is this? A Rectangle

copyright©amberpasillas2010 AAA What is the formula for the area of a triangle ? We can use the formula for area of a rectangle to find the formula for area of a triangle. Two triangles make one rectangle. We want to find half of the area of the rectangle. base height b h

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copyright©amberpasillas2010 base height h This holds true for any triangle.

copyright©amberpasillas2010 A triangle is half the area of a rectangle. To find the area of a triangle, you use the rectangle formula (base times height) and divide it in half. A = base height 2 5 m 12 m 13 m A = = 30 m 2

copyright©amberpasillas cm 5 cm8 cm Perimeter Area P = a + b + c P = P = 24 cm 3 cm Find the perimeter a nd area of this triangle.

copyright©amberpasillas2010 7in 2 cm 6 in 9 cm 4 m 13 mm 11 m 8mm

copyright©amberpasillas2010 Backpack. You are making a reflective patch for your backpack. The patch is a triangle with a base of 12 cm and a height of 6 cm. What is the area of the patch?

copyright©amberpasillas2010 Draw a parallelogram with a base of 5cm and a height of 3 cm in your Math journal. Note: The height is NOT the same as the width. 5 cm 3 cm

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Given the formula for area of a triangle and the formula for area of a parallelogram we are going to use that information to discover the formula for the area of a trapezoid Watch carefully not to miss it!

This trapezoid is regular. regular trapezoid This trapezoid is an irregular trapezoid. irregular trapezoid Also known as an isosceles trapezoid

copyright©amberpasillas2010 b2b2 b1b1 h Copy that trapezoid, flip it over, and put it next to the original b 2 b 1 h Give the height, base 1 & base 2 (b 1 + b 2 ) h What polygon is it now? Parallelogram

copyright©amberpasillas2010 Notice that the trapezoid is half the area of the parallelogram. (b 1 + b 2 ) h Given our original trapezoid put together with a similar flipped trapezoid, we found it made a parallelogram. We are going to use the area of a parallelogram to find the area of a trapezoid. It takes two trapezoids to make one parallelogram.

copyright©amberpasillas2010 (b 1 + b 2 ) h Parallelogram Trapezoid Notice that the trapezoid is half the area of the parallelogram. How do we find half the area ? 2 A = (b 1 + b 2 ) h Hint: Think of area of a triangle.

copyright©amberpasillas2010 Area of Trapezoid 2 in 6 in 3 in = 12 in 2 2 A = (b 1 + b 2 ) h 4 in

copyright©amberpasillas2010 Area of Trapezoid 3 m 8 m 4 m = 22 m 2 2 A = (b 1 + b 2 ) h 5 m

copyright©amberpasillas in 5 in 7 in 6 in Here is another way to look at the trapezoid formula. Instead of dividing by 2, multiply by ½

copyright©amberpasillas2010 The End! Practice in your Journal !

copyright©amberpasillas2010 # 1 Area of a Trapezoid 5 ft 4 ft A = (b 1 + b 2 ) x h 2 3 ft A = (4 + 5) x 3 2 A = (9) x = 13.5 ft 2 A = (base 1 + base 2 ) x height 2 =

copyright©amberpasillas2010 Area of Polygons #2 The Area of a figure is the number of square units needed to cover it. Rectangle Parallelogram Triangle 5 8 7

copyright©amberpasillas2010 Practice Complete the practice worksheet. Work in your groups.

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