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Area of a Trapezoid

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**Today we are going to review Area of a Triangle & Parallelogram.**

Then we are going to discover the Area of a Trapezoid.

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**Watch carefully not to miss it!**

Area of a Triangle 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!

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Area of a Triangle Given a right triangle Make a similar triangle,

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**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

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**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. height h base b What is the formula for the area of a triangle?

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**This holds true for any triangle**

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

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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

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**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 = P = 24 cm

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**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!

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**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

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**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) Give the height, base 1 & base 2 Copy that trapezoid, flip it over, and put it next to the original

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**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.

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**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

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

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

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**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

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**Take out your study guide!**

Area of a Trapezoid The End! Take out your study guide!

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**Area of a Trapezoid A = (b1 + b2) x h A = (4 + 5) x 3 2 A = (9) x 3 27**

# 5 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

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Area of Polygons #6 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

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To see all math formulas correctly you need to install MathType software, similar to equation editor and is available for free at Design Science website .

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