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Polygons

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Polygons

1. 1. Finding the Area of Polygons Rectangles Parallelograms Triangles Trapezoids
2. 2. Review: Perimeter <ul><li>Perimeter is the distance around a figure. </li></ul><ul><li>To calculate perimeter, add up the lengths of the sides. </li></ul><ul><li>Using your ruler, measure the perimeter of your rectangle. </li></ul>
3. 3. What is the Perimeter of Your Rectangle? <ul><li>24 inches </li></ul><ul><li>20 inches </li></ul><ul><li>22 inches </li></ul><ul><li>18 inches </li></ul>
4. 4. Area <ul><li>Area is the amount of space a figure takes up. </li></ul><ul><li>Area is measured in square units . </li></ul><ul><li>Draw a grid on your rectangle so that you can count the number of square units . </li></ul>
5. 5. What is the area of your rectangle? <ul><li>24 square inches </li></ul><ul><li>20 square inches </li></ul><ul><li>22 square inches </li></ul><ul><li>18 square inches </li></ul>
6. 6. Can you think of an easier way to count the squares? <ul><li>If you multiply the number of squares going across times the number of square going down, you get 24. </li></ul><ul><li>The formula for the area of a rectangle is: Area = Length x Width </li></ul>
7. 7. Parallelogram <ul><li>Using scissors, cut a 45 degree diagonal line starting in one corner of your rectangle. </li></ul><ul><li>Take the piece you cut off and move it to the other side. </li></ul><ul><li>Now you have a parallelogram! </li></ul><ul><li>What is the area of this parallelogram? Think: Have we changed the area? </li></ul>
8. 8. Trapezoid <ul><li>See if you can make a trapezoid using the same 2 pieces. </li></ul><ul><li>Have we changed the area? </li></ul>
9. 9. Trapezoid Area Formula <ul><li>Average the lengths of the bases. To do this: </li></ul><ul><li>1. Add the lengths of the bases together. </li></ul><ul><li>2. Divide by 2. </li></ul><ul><li>Multiply by the height. </li></ul><ul><li>Did you get 24? </li></ul>
10. 10. Triangle <ul><li>Cut your “original” rectangle in half diagonally to make 2 triangles. </li></ul><ul><li>What do you notice about these 2 triangles? </li></ul>
11. 11. What do you notice about these 2 triangles? <ul><li>They are congruent. </li></ul><ul><li>They are right triangles. </li></ul><ul><li>They are scalene triangles. </li></ul><ul><li>All of the above are true. </li></ul>
12. 12. Triangle Area Formula <ul><li>Every triangle is half of a parallelogram. Therefore, the formula is: </li></ul><ul><li>Base x Height </li></ul><ul><li>2 </li></ul>
13. 13. 1) What formula should we use? <ul><li>bh </li></ul><ul><li>½ bh </li></ul><ul><li>½ (b1 +b2)h </li></ul>
14. 14. 2) What formula should we use? <ul><li>bh </li></ul><ul><li>½ bh </li></ul><ul><li>½ (b1 +b2)h </li></ul>
15. 15. 3) What formula should we use? <ul><li>bh </li></ul><ul><li>½ bh </li></ul><ul><li>½ (b1 +b2)h </li></ul>
16. 16. 4) What formula should we use? <ul><li>bh </li></ul><ul><li>½ bh </li></ul><ul><li>½ (b1 +b2)h </li></ul>