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Area Formulas

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**What is the area formula?**

Rectangle What is the area formula?

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**What is the area formula?**

Rectangle What is the area formula? b h

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**What is the area formula?**

Rectangle What is the area formula? bh What other shape has 4 right angles?

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**What is the area formula?**

Rectangle What is the area formula? bh Square! What other shape has 4 right angles?

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**What is the area formula?**

Rectangle What is the area formula? bh Square! What other shape has 4 right angles? Can we use the same area formula?

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**What is the area formula?**

Rectangle What is the area formula? bh Square! What other shape has 4 right angles? Can we use the same area formula? Yes

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Practice! 17m Rectangle 10m Square 14cm

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Answers 17m Rectangle 10m 170 m2 Square 196 cm2 14cm

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**So then what happens if we cut a rectangle in half?**

What shape is made?

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**So then what happens if we cut a rectangle in half?**

Triangle So then what happens if we cut a rectangle in half? What shape is made?

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**So then what happens if we cut a rectangle in half?**

Triangle So then what happens if we cut a rectangle in half? What shape is made? 2 Triangles

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**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?

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**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?

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**Triangle So then what happens if we cut a rectangle in half?**

What shape is made? 2 Triangles bh So then what happens to the formula?

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**Triangle So then what happens if we cut a rectangle in half?**

What shape is made? 2 Triangles bh 2 So then what happens to the formula?

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Practice! Triangle 8 m 5 m

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Answers Triangle 8 m 20 m2 5 m

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**Let’s look at a parallelogram.**

What happens if we slice off the slanted parts on the ends?

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**Let’s look at a parallelogram.**

What happens if we slice off the slanted parts on the ends?

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**Let’s look at a parallelogram.**

What happens if we slice off the slanted parts on the ends?

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**Let’s look at a parallelogram.**

What happens if we slice off the slanted parts on the ends?

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**Let’s look at a parallelogram.**

What happens if we slice off the slanted parts on the ends?

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**Let’s look at a parallelogram.**

What happens if we slice off the slanted parts on the ends?

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**Let’s look at a parallelogram.**

What happens if we slice off the slanted parts on the ends?

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**Let’s look at a parallelogram.**

What happens if we slice off the slanted parts on the ends?

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**Let’s look at a parallelogram.**

What happens if we slice off the slanted parts on the ends?

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**Let’s look at a parallelogram.**

What happens if we slice off the slanted parts on the ends?

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**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?

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**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? b h

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Parallelogram Be careful though! The height has to be perpendicular from the base, just like the side of a rectangle! b h

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Parallelogram Be careful though! The height has to be perpendicular from the base, just like the side of a rectangle! b h

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Parallelogram Be careful though! The height has to be perpendicular from the base, just like the side of a rectangle! b h

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**Let’s try something new with the parallelogram.**

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**Let’s try something new with the parallelogram.**

Earlier, you saw that you could use two trapezoids to make a parallelogram.

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**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.

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Trapezoid

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Trapezoid

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Trapezoid So we see that we are dividing the parallelogram in half. What will that do to the formula?

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Trapezoid So we see that we are dividing the parallelogram in half. What will that do to the formula? b h

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Trapezoid So we see that we are dividing the parallelogram in half. What will that do to the formula? b h 2

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**But now there is a problem. What is wrong with the base?**

Trapezoid But now there is a problem. What is wrong with the base? b h 2

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Trapezoid 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. b h 2

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Trapezoid 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 (b1 + b2) h 2

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Practice! 3 m Trapezoid 5 m 7 m

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Answers 3 m Trapezoid 25 m2 5 m 7 m (3 m + 7 m) 5m 2

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Summary! b h b h (b1 + b2) h 2 2

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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.

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.

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