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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)

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

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 = 5 12 2 = 30 m 2

copyright©amberpasillas2010 11 cm 5 cm8 cm Perimeter Area P = a + b + c P = 5 + 8 + 11 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

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©amberpasillas2010 4 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 # 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 3 2 27 2 = 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 4 5 10 78 Parallelogram Triangle 5 8 7