What you will learn? Formulas for finding the areas of rectangles, parallelograms, triangles, trapezoids, kites, regular polygons, and circles by cutting apart and rearranging these figures.

Area is the amount of surface space that a flat object has. Area is reported in the amount of square units.

When you measure the amount of carpet to cover the floor of a room, you measure it in square units. Would the area of your bedroom or the area of your house be greater? You’re right! The area of your house is greater than the area of your bedroom.

Area = 15 square feet Lets find the area of this surface if each square is equal to one foot. Count the number of squares

Count the number of squares to determine the area of this surface. What is the area? The area is equal to 9 square units. Try this one!

Rectangle What is the area formula? Area Formulas

Square What other shape has 4 right angles? Area Formulas Can we use the same area formula? Yes

Practice! Rectangle Square 10m 17m 14cm Area Formulas

Answers Rectangle Square 10m 17m 14cm 196 cm m 2 Area Formulas

So then what happens if we cut a rectangle in half? What shape is made? Area Formulas Triangle 2 Triangles So then what happens to the formula?

Practice! Triangle 5 ft 14 ft Area Formulas

Answers 35 ft 2 Triangle 5 ft 14 ft Area Formulas

Summary so far... bh Area Formulas

Summary so far... bh Area Formulas

Summary so far... bh Area Formulas

Summary so far... bh Area Formulas

Summary so far... bh 2 Area Formulas

Parallelogram Let’s look at a parallelogram. Area Formulas

Parallelogram Let’s look at a parallelogram. What happens if we slice off the slanted parts on the ends? Area Formulas

Parallelogram What happens if we move one part to the end? Area Formulas What will the area formula be now that it is a rectangle? b.h

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

Rhombus The rhombus is just a parallelogram with all equal sides! So it also has bh for an area formula. Area Formulas b.h

Practice! Parallelogram Rhombus 3 in 9 in 4 cm 2.7 cm Area Formulas

Answers 10.8 cm 2 27 in 2 Parallelogram Rhombus 3 in 9 in 4 cm 2.7 cm Area Formulas

Let’s try something new with the parallelogram. Area Formulas You can 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 Area Formulas So we see that we are dividing the parallelogram in half. What will that do to the formula?

Trapezoid But now there is a problem. What is wrong with the base? Area Formulas

Trapezoid By adding them together, we get the original base from the parallelogram. So we need to account for the split base, by calling the top base, base 1 and the bottom base, base 2 Area Formulas base 1 base 2 The heights are the same, so no problem there. (b1+ b2) h 2

Practice! Trapezoid 11 m 3 m 5 m Area Formulas

Answers 35 m 2 Trapezoid 11 m 3 m 5 m Area Formulas

Summary so far... bh

Summary so far... bh

Summary so far... bh

Summary so far... bh

Summary so far... bh 2

Summary so far... bh 2

Summary so far... bh 2

Summary so far... bh 2

Summary so far... bh 2

Summary so far... bh 2

Summary so far... bh 2

Summary so far... bh 2

Summary so far... bh 2

Summary so far... bh 2

Summary so far... bh 2 (b1 + b2)h 2

Summary so far... bh 2 (b1 + b2)h 2

Summary so far... bh 2 (b1 + b2)h 2

Summary so far... bh 2 (b1 + b2)h 2

Summary so far... bh 2 (b1 + b2)h 2

Summary so far... bh 2 (b1 + b2)h 2

So there is just one more left! Let’s go back to the triangle.You know that by reflecting a triangle, you can make a kite. Area Formulas Kite

Now we have to determine the formula. What is the area of a triangle formula again? Area Formulas

Kite Now we have to determine the formula. What is the area of a triangle formula again? bhbh 2 Area Formulas Fill in the blank. A kite is made up of __?__ triangles. So it seems we should multiply the formula by 2.

Kite bhbh 2 *2 = bhbh Area Formulas

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. bhbh 2. 2 = bhbh Area Formulas

Kite Let’s use kite vocabulary instead to create our formula. b = Symmetry Line h = Half the Other Diagonal Area Formulas Symmetry Line * Half the Other Diagonal

Practice! Kite 2 ft 10 ft Area Formulas

Answers 20 ft 2 Kite 2 ft 10 ft Area Formulas

Summary so far... bh

Summary so far... bh

Summary so far... bh

Summary so far... bh

Summary so far... bh 2

Summary so far... bh 2

Summary so far... bh 2

Summary so far... bh 2

Summary so far... bh 2

Summary so far... bh 2

Summary so far... bh 2

Summary so far... bh 2

Summary so far... bh 2

Summary so far... bh 2

Summary so far... bh 2 (b1 + b2)h 2

Summary so far... bh 2 (b1 + b2)h 2

Summary so far... bh 2 (b1 + b2)h 2

Summary so far... bh 2 (b1 + b2)h 2

Summary so far... bh 2 (b1 + b2)h 2

Summary so far... bh 2 (b1 + b2)h 2

Summary so far... bh 2 (b1 + b2)h 2

Summary so far... bh 2 (b1 + b2)h 2

Summary so far... bh 2 (b1 + b2)h 2

Summary so far... bh 2 (b1 + b2)h 2 Symmetry Line * Half the Other Diagonal

Final Summary Make sure all your formulas are written down! bhbh bhbh 2 (b1 + b2)h 2 Symmetry Line * Half the Other Diagonal