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Area of a Parallelogram

Area of a Triangle. and. Area of a Parallelogram. Polygons. Today we are going to find the Area of Parallelograms and the Area of Triangles. Polygons. Area. The number of square units that are needed to cover the surface of a figure. Polygon. Any straight-sided closed plane figure.

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Area of a Parallelogram

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  1. Area of a Triangle and Area of a Parallelogram

  2. Polygons Today we are going to find the Area ofParallelogramsand the Area ofTriangles

  3. Polygons Area • The number of square units that are needed to cover the surface of a figure. Polygon Any straight-sided closed plane figure.

  4. Polygons Circle the polygons below. Regular Polygon Polygon with all sides congruent and all angles congruent.

  5. # of sides Polygons Regular Polygons Polygons Picture Picture Name Name 3 Acute Equilateral Triangle 4 Quadrilateral Square Regular Pentagon 5 Pentagon Regular Hexagon 6 Hexagon

  6. # of sides Polygons Regular Polygons Polygons Picture Picture Name Name 7 Heptagon 8 Regular Octagon Octagon 9 Nonagon 10 Regular Decagon Decagon

  7. Area of a Rectangle The area of a rectangle is equal to the base times the height. Also known as length times width. height A = bh (h) (b) base A = bh is the same as A = lw

  8. Area of a Rectangle What is the area of the rectangle? 2 2 in. x 6 12 in.2 6 in. 12 in2 or square inches

  9. Area of a Square A square is a special rectangle. Since the base and the height are the same size, we call them sides (s) instead of base and height. A= s2 s height = s s base = s

  10. Area of a Square What is the area of the square? 4 4 m. 4 x 16 m.2 4 m. 16m2 or square meters

  11. Area of a Parallelogram Given the formula for area of a rectangle, we are going to use that information to derive the formula for the area of a parallelogram Watch carefully not to miss it!

  12. Area of a Parallelogram Draw a straight line from the top corner perpendicular to the base Cut that triangle and move it to the other side What shape does it make? Rectangle

  13. Area of a Parallelogram Use this information to find thearea of a parallelogram h height = h h b base = b A parallelogram has the same area as a rectangle! What is the formula forarea of a parallelogram?

  14. Area of a Parallelogram 2 cm. 90º 4 cm. = 8 cm.2 Check to see if you got it right.

  15. Area of a Parallelogram 2 cm. 90º 4 cm. = 8 cm.2 Cut off the piece at the dotted line.

  16. Area of a Parallelogram 2 cm. 90º 4 cm. = 8 cm.2 Cut off the piece at the dotted line.

  17. Area of a Parallelogram 2 cm. 90º 4 cm. = 8 cm.2 Move this piece to the other side.

  18. Area of a Parallelogram 2 cm. 90º 4 cm. = 8 cm.2 Move this piece to the other side.

  19. Area of a Parallelogram Let’s check it with the area of a rectangle. 2 cm. 90º 4 cm. = 8 cm.2 Now you have a rectangle How many squares do you see? A = 8square cm. or 8 cm.2

  20. Area of a Parallelogram What is the area of this parallelogram? 5 5 cm. 7 x 35 cm.2 7 cm. 35 square centimeters or 35 cm.2

  21. Area of a Parallelogram What is the area of this parallelogram? 5 6 x 5 ft. 30 ft.2 6 ft. 30 square feet or 30 ft.2

  22. 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!

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

  24. 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

  25. Area of a Triangle We can use the formula for area of a rectangle to find the formula for area of a triangle. Twotriangles make one rectangle. We want to find half of the area of the rectangle. height h base b Whatis the formula for the area of a triangle?

  26. Area of a Triangle When we put 2 right triangles together is made a rectangle. Watch what happens when instead we use 2 isosceles triangles.

  27. Area of a Triangle Given an isosceles triangle Make a similar triangle,

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

  29. height h base Area of a Triangle How do you find the area of the parallelogram?

  30. Area of a Triangle 5 cm 6 cm 3 cm 9 cm

  31. Area of a Triangle The End! Take out your study guide!

  32. Area of a Parallelogram # 3 To find the area for a parallelogram use what you know about area of a rectangle. A = base x height 3 in A = b x h 5 in A = 5 x 3 = 15 in2

  33. Area of a Triangle # 4 A triangle is half the area of a rectangle. To find the area of a triangle you use the rectangle formula and divide it in half. A = base x height 2 6 m 8 m A = 8 x 6 = 24 m2 2

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