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Area formulas
 

Area formulas

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Area formulas By Deepak Kumar

Area formulas By Deepak Kumar

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    Area formulas Area formulas Presentation Transcript

    •  
    • Area Formulas Mr. Deepak Kumar
    • Rectangle
    • Rectangle What is the area formula?
    • Rectangle What is the area formula? bh
    • Rectangle What is the area formula? bh What other shape has 4 right angles?
    • Rectangle What is the area formula? bh What other shape has 4 right angles? Square!
    • Rectangle What is the area formula? bh What other shape has 4 right angles? Square! Can we use the same area formula?
    • Rectangle What is the area formula? bh What other shape has 4 right angles? Square! Can we use the same area formula? Yes
    • Practice! Rectangle Square 10m 17m 14cm
    • Answers Rectangle Square 10m 17m 14cm 196 cm 2 170 m 2
    • So then what happens if we cut a rectangle in half? What shape is made?
    • Triangle So then what happens if we cut a rectangle in half? What shape is made?
    • Triangle So then what happens if we cut a rectangle in half? What shape is made? 2 Triangles
    • Triangle So then what happens if we cut a rectangle in half? What shape is made? 2 Triangles So then what happens to the formula?
    • Triangle So then what happens if we cut a rectangle in half? What shape is made? 2 Triangles So then what happens to the formula?
    • Triangle So then what happens if we cut a rectangle in half? What shape is made? 2 Triangles So then what happens to the formula? bh
    • Triangle So then what happens if we cut a rectangle in half? What shape is made? 2 Triangles So then what happens to the formula? bh 2
    • Practice! Triangle 5 ft 14 ft
    • Answers 35 ft 2 Triangle 5 ft 14 ft
    • Summary so far...
      • bh
    • Summary so far...
      • bh
    • Summary so far...
      • bh
    • Summary so far...
      • bh
      bh
    • Summary so far...
      • bh
      bh 2
    • Parallelogram Let’s look at a parallelogram.
    • Parallelogram Let’s look at a parallelogram. What happens if we slice off the slanted parts on the ends?
    • Parallelogram Let’s look at a parallelogram. What happens if we slice off the slanted parts on the ends?
    • Parallelogram Let’s look at a parallelogram. What happens if we slice off the slanted parts on the ends?
    • Parallelogram Let’s look at a parallelogram. What happens if we slice off the slanted parts on the ends?
    • Parallelogram Let’s look at a parallelogram. What happens if we slice off the slanted parts on the ends?
    • Parallelogram Let’s look at a parallelogram. What happens if we slice off the slanted parts on the ends?
    • Parallelogram Let’s look at a parallelogram. What happens if we slice off the slanted parts on the ends?
    • Parallelogram Let’s look at a parallelogram. What happens if we slice off the slanted parts on the ends?
    • Parallelogram Let’s look at a parallelogram. What happens if we slice off the slanted parts on the ends?
    • Parallelogram Let’s look at a parallelogram. What happens if we slice off the slanted parts on the ends?
    • Parallelogram Let’s look at a parallelogram. What happens if we slice off the slanted parts on the ends? What will the area formula be now that it is a rectangle?
    • Parallelogram Let’s look at a parallelogram. What happens if we slice off the slanted parts on the ends? What will the area formula be now that it is a rectangle? bh
    • Parallelogram Be careful though! The height has to be perpendicular from the base, just like the side of a rectangle! bh
    • Parallelogram Be careful though! The height has to be perpendicular from the base, just like the side of a rectangle! bh
    • Parallelogram Be careful though! The height has to be perpendicular from the base, just like the side of a rectangle! bh
    • Rhombus The rhombus is just a parallelogram with all equal sides! So it also has bh for an area formula. bh
    • Practice! Parallelogram Rhombus 3 in 9 in 4 cm 2.7 cm
    • Answers 10.8 cm 2 27 in 2 Parallelogram Rhombus 3 in 9 in 4 cm 2.7 cm
    • Let’s try something new with the parallelogram.
    • Let’s try something new with the parallelogram. Earlier, you saw that you could use two trapezoids to make a parallelogram.
    • Let’s try something new with the parallelogram. Earlier, you saw that you could use two trapezoids to make a parallelogram. Let’s try to figure out the formula since we now know the area formula for a parallelogram.
    • Trapezoid
    • Trapezoid
    • Trapezoid So we see that we are dividing the parallelogram in half. What will that do to the formula?
    • Trapezoid So we see that we are dividing the parallelogram in half. What will that do to the formula? bh
    • Trapezoid So we see that we are dividing the parallelogram in half. What will that do to the formula? bh 2
    • Trapezoid But now there is a problem. What is wrong with the base? bh 2
    • Trapezoid b h 2 So we need to account for the split base, by calling the top base, base 1 , and the bottom base, base 2 . By adding them together, we get the original base from the parallelogram. The heights are the same, so no problem there.
    • Trapezoid ( b1 + b2 ) h 2 So we need to account for the split base, by calling the top base, base 1 , and the bottom base, base 2 . By adding them together, we get the original base from the parallelogram. The heights are the same, so no problem there. base 2 base 1 base 1 base 2
    • Practice! Trapezoid 11 m 3 m 5 m
    • Answers 35 m 2 Trapezoid 11 m 3 m 5 m
    • Summary so far...
      • bh
    • Summary so far...
      • bh
    • Summary so far...
      • bh
    • Summary so far...
      • bh
      bh
    • Summary so far...
      • bh
      bh 2
    • Summary so far...
      • bh
      bh 2
    • Summary so far...
      • bh
      bh 2
    • Summary so far...
      • bh
      bh 2
    • Summary so far...
      • bh
      bh 2
    • Summary so far...
      • bh
      bh 2
    • Summary so far...
      • bh
      bh 2
    • Summary so far...
      • bh
      bh 2
    • Summary so far...
      • bh
      bh 2
    • Summary so far...
      • bh
      bh 2
    • Summary so far...
      • bh
      bh 2 ( b1 + b2 ) h 2
    • Summary so far...
      • bh
      bh 2 ( b1 + b2 ) h 2
    • Summary so far...
      • bh
      bh 2 ( b1 + b2 ) h 2
    • Summary so far...
      • bh
      bh 2 ( b1 + b2 ) h 2
    • Summary so far...
      • bh
      bh 2 ( b1 + b2 ) h 2
    • Summary so far...
      • bh
      bh 2 ( b1 + b2 ) h 2
    • So there is just one more left!
    • So there is just one more left! Let’s go back to the triangle. A few weeks ago you learned that by reflecting a triangle, you can make a kite.
    • Kite So there is just one more left! Let’s go back to the triangle. A few weeks ago you learned that by reflecting a triangle, you can make a kite.
    • Kite Now we have to determine the formula. What is the area of a triangle formula again?
    • Kite Now we have to determine the formula. What is the area of a triangle formula again? b h 2
    • Kite Now we have to determine the formula. What is the area of a triangle formula again? b h 2 Fill in the blank. A kite is made up of ____ triangles.
    • Kite Now we have to determine the formula. What is the area of a triangle formula again? b h 2 Fill in the blank. A kite is made up of ____ triangles. So it seems we should multiply the formula by 2.
    • Kite b h 2 *2 = b h
    • Kite Now we have a different problem. What is the base and height of a kite? The green line is called the symmetry line, and the red line is half the other diagonal. b h 2 *2 = b h
    • Kite Let’s use kite vocabulary instead to create our formula. Symmetry Line* Half the Other Diagonal
    • Practice! Kite 2 ft 10 ft
    • Answers 20 ft 2 Kite 2 ft 10 ft
    • Summary so far...
      • bh
    • Summary so far...
      • bh
    • Summary so far...
      • bh
    • Summary so far...
      • bh
      bh
    • Summary so far...
      • bh
      bh 2
    • Summary so far...
      • bh
      bh 2
    • Summary so far...
      • bh
      bh 2
    • Summary so far...
      • bh
      bh 2
    • Summary so far...
      • bh
      bh 2
    • Summary so far...
      • bh
      bh 2
    • Summary so far...
      • bh
      bh 2
    • Summary so far...
      • bh
      bh 2
    • Summary so far...
      • bh
      bh 2
    • Summary so far...
      • bh
      bh 2
    • Summary so far...
      • bh
      bh 2 ( b1 + b2 ) h 2
    • Summary so far...
      • bh
      bh 2 ( b1 + b2 ) h 2
    • Summary so far...
      • bh
      bh 2 ( b1 + b2 ) h 2
    • Summary so far...
      • bh
      bh 2 ( b1 + b2 ) h 2
    • Summary so far...
      • bh
      bh 2 ( b1 + b2 ) h 2
    • Summary so far...
      • bh
      bh 2 ( b1 + b2 ) h 2
    • Summary so far...
      • bh
      bh 2 ( b1 + b2 ) h 2
    • Summary so far...
      • bh
      bh 2 ( b1 + b2 ) h 2
    • Summary so far...
      • bh
      bh 2 ( b1 + b2 ) h 2
    • Summary so far...
      • bh
      bh 2 ( b1 + b2 ) h 2 Symmetry Line * Half the Other Diagonal
    • Final Summary Make sure all your formulas are written down!
      • b h
      b h 2 ( b1 + b2 ) h 2 Symmetry Line * Half the Other Diagonal