Area Formulas
Rectangle
What is the area formula? Rectangle What is the area formula?
What is the area formula? Rectangle What is the area formula? bh
What is the area formula? Rectangle What is the area formula? bh What other shape has 4 right angles?
What is the area formula? Rectangle What is the area formula? bh Square! What other shape has 4 right angles?
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?
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
Practice! 17m Rectangle 10m Square 14cm
Answers 17m Rectangle 10m 170 m2 Square 196 cm2 14cm
So then what happens if we cut a rectangle in half? What shape is made?
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?
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
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 bh 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 bh 2 So then what happens to the formula?
Practice! Triangle 14 ft 5 ft
Answers Triangle 14 ft 35 ft2 5 ft
Summary so far... bh
Summary so far... bh
Summary so far... bh
Summary so far... bh bh
Summary so far... bh bh 2
Let’s look at a parallelogram.
Let’s look at a parallelogram. What happens if we slice off the slanted parts on the ends?
Let’s look at a parallelogram. What happens if we slice off the slanted parts on the ends?
Let’s look at a parallelogram. What happens if we slice off the slanted parts on the ends?
Let’s look at a parallelogram. What happens if we slice off the slanted parts on the ends?
Let’s look at a parallelogram. What happens if we slice off the slanted parts on the ends?
Let’s look at a parallelogram. What happens if we slice off the slanted parts on the ends?
Let’s look at a parallelogram. What happens if we slice off the slanted parts on the ends?
Let’s look at a parallelogram. What happens if we slice off the slanted parts on the ends?
Let’s look at a parallelogram. What happens if we slice off the slanted parts on the ends?
Let’s look at a parallelogram. What happens if we slice off the slanted parts on the ends?
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?
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! 9 in Parallelogram 3 in Rhombus 2.7 cm 4 cm
Answers 9 in Parallelogram 27 in2 3 in Rhombus 2.7 cm 10.8 cm2 4 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
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? bh 2
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. bh 2
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
Practice! 3 m Trapezoid 5 m 11 m
Answers 3 m Trapezoid 35 m2 5 m 11 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 (b1 + b2)h 2 2
Summary so far... bh bh (b1 + b2)h 2 2
Summary so far... bh bh (b1 + b2)h 2 2
Summary so far... bh bh (b1 + b2)h 2 2
Summary so far... bh bh (b1 + b2)h 2 2
Summary so far... bh bh (b1 + b2)h 2 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.
So there is just one more left! 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? bh 2
Fill in the blank. A kite is made up of ____ triangles. Now we have to determine the formula. What is the area of a triangle formula again? bh 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? bh 2 Fill in the blank. A kite is made up of ____ triangles. So it seems we should multiply the formula by 2.
Kite bh bh *2 = 2
Kite bh bh *2 = 2 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.
Let’s use kite vocabulary instead to create our formula. Symmetry Line*Half the Other Diagonal
Practice! Kite 2 ft 10 ft
Answers Kite 20 ft2 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 (b1 + b2)h 2 2
Summary so far... bh bh (b1 + b2)h 2 2
Summary so far... bh bh (b1 + b2)h 2 2
Summary so far... bh bh (b1 + b2)h 2 2
Summary so far... bh bh (b1 + b2)h 2 2
Summary so far... bh bh (b1 + b2)h 2 2
Summary so far... bh bh (b1 + b2)h 2 2
Summary so far... bh bh (b1 + b2)h 2 2
Summary so far... bh bh (b1 + b2)h 2 2
Summary so far... bh bh (b1 + b2)h 2 2 Symmetry Line * Half the Other Diagonal
Final Summary Make sure all your formulas are written down! bh bh (b1 + b2)h 2 2 Symmetry Line * Half the Other Diagonal