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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.
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 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
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 = 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 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 The End! Take out your study guide!
copyright©amberpasillas2010 # 5 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 #6 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
Area of a Parallelogram
Area of a Trapezoid.
Triangles, Quadrilaterals, Nets, Prisms & Composite Polygons
Copyright©amberpasillas2010. Remove all other thoughts from your mind. Pay close attention. Try all the examples. Ignore all other distractions.
1 Lesson Areas of Polygons. 2 Lesson Areas of Polygons California Standard: Measurement and Geometry 1.2 Use formulas routinely for finding.
8cm 5cm Area = 8 x 5 = 40cm 2 A parallelogram can be split up into a rectangle and 2 triangles – each with the same area. 10cm 5cm.
copyright©amberpasillas2010 Good morning!! Thank you for taking the opportunity to improve your grade!!! Please follow these directions: 1.Take a seat.
Area of 2D shapes. Quadrilaterals A quadrilateral is a geometric figure that is made up of four line segments, called sides, that intersect only at their.
Area of Rectangles, Squares, Parallelograms, Triangles, and Trapezoids.
Copyright©amberpasillas2010. Perimeter – (P) (P) The distance around a figure. 10 ft. 6 ft ft.
Area of Trapezoids. A trapezoid can be thought of as half of a parallelogram also. Notice that when we put the 2 trapezoids together we get a parallelogram.
$100 Area of Parallelograms Area of Triangles Perimeter And Area Area of Trapezoids Area of Compound Figures & Area and Circumference of Circles $200.
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Finding the Area of Polygons Vocabulary Perimeter – The sum of all sides of the shape. Area – The total occupied space of a shape in units squared.
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= (2 in) · (2 in) = 4 in 2. P = a + b + c A = ½(8*8) A = 32 P = =20.
Perimeter & Area Lessons 19 & 20.
9-4 Area of Triangles and Trapezoids Course 2 Warm Up Warm Up Problem of the Day Problem of the Day Lesson Presentation Lesson Presentation.
Area of Triangles and Trapezoids base altitude base.
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