Materials: Journal, a pencil, and a metric ruler. Area of Polygons 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? Materials: Journal, a pencil, and a metric ruler.

Review and focus: Find the area and perimeter of the following figures Review and focus: Find the area and perimeter of the following figures. Name the figures. 9mm 9mm 8 ft 4 ft

Review and focus: Find the area and perimeter of the following figures. x x 7 ft 4.5 ft

Area of a Triangle  

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

We can use the formula for area of a rectangle 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. AAA height     h base b What is the formula for the area of a triangle?

This holds true for any triangle. Area of a Triangle This holds true for any triangle. height h   base

Area of a Triangle 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 13 m 12 m 5 m A = 5 • 12 = 30 m2 2

Area of a Triangle Area Perimeter Find the perimeter and area of this triangle. 5 cm 8 cm Area 3 cm 11 cm Perimeter P = a + b + c P = 5 + 8 + 11 P = 24 cm

Area of Polygons 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 open to homework, a pencil, glue, and a metric ruler.

Find the area of the triangles in your Journals. 7in 2 cm 6 in 9 cm 4 m 13 mm 11 m 8mm

Area of a Triangle 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?

Area of a Parallelogram 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. 3 cm 5 cm

Area of a Parallelogram

Area of a Parallelogram

Area of a Parallelogram

Find the area of the parallelograms in your Journal.

Communicate your understanding

Watch carefully not to miss it! Area of a Trapezoid 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. Area of a Trapezoid This trapezoid is regular. regular trapezoid Also known as an isosceles trapezoid This trapezoid is an irregular trapezoid. irregular trapezoid

Copy that trapezoid, flip it over, and put it next to the original Area of a Trapezoid b2 b1 h b1 What polygon is it now? h h Parallelogram b2 (b1 + b2) Given the height, base 1 & base 2 Copy that trapezoid, flip it over, and put it next to the original

Area of a Trapezoid h (b1 + b2) put together with a similar flipped trapezoid, we found it made a parallelogram. Given our original trapezoid h (b1 + b2) We are going to use the area of a parallelogram to find the area of a trapezoid. Notice that the trapezoid is half the area of the parallelogram. It takes two trapezoids to make one parallelogram.

Trapezoid Parallelogram Area of a Trapezoid h (b1 + b2) Notice that the trapezoid is half the area of the parallelogram. How do we find half the area? h Hint: Think of area of a triangle. (b1 + b2) Trapezoid Parallelogram A = (b1 + b2) • h 2

Area of Trapezoid Area of a Trapezoid 2 in 4 in A = (b1 + b2) • h 3 in

Area of Trapezoid Area of a Trapezoid 3 m 5 m A = (b1 + b2) • h 4 m 2

Area of a Trapezoid 5 in 4 in 6 in 7 in Here is another way to look at the trapezoid formula. Instead of dividing by 2, multiply by ½

The End! Have a great weekend!! Area of a Trapezoid The End! Have a great weekend!!

Area of a Trapezoid A = (b1 + b2) x h A = (4 + 5) x 3 2 A = (9) x 3 27 # 1 4 ft A = (base1 + base2) x height 3 ft 2 A = (b1 + b2) x h 5 ft 2 A = (4 + 5) x 3 2 A = (9) x 3 27 = = 13.5 ft2 2 2

Area of Polygons #2 The Area of a figure is the number of square units needed to cover it. Rectangle Parallelogram Triangle 7 4 8 7 5 5 10 8

Practice Complete the practice worksheet. Work in your groups.

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