AREA

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

AREA

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.

1 2

3

4 5 6 7 8

9 10 11 12 13 14

15

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!

1

5

2

4

7

3

6

8 9

Rectangle

What is the area formula?

Area Formulas

b.h

SquareWhat other shape has 4 right

angles?

Area Formulas

Can we use the same area formula?

Yes

b.h

Practice!Rectangle

Square

10m

17m

14cm

Area Formulas

AnswersRectangle

Square

10m

17m

14cm

196 cm2

170 m2

Area Formulas

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

What shape is made?

Area Formulas

Triangle2 Triangles

So then what happens to the formula?

b.h

2

Practice!Triangle

5 ft

14 ft

Area Formulas

Answers

35 ft2Triangle5 ft

14 ft

Area Formulas

Summary so far...

bh

Area Formulas

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bh

Area Formulas

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bh

Area Formulas

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bh bh

Area Formulas

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bh bh2

Area Formulas

ParallelogramLet’s look at a parallelogram.

Area Formulas

ParallelogramLet’s look at a parallelogram.

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

Area Formulas

ParallelogramWhat 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

ParallelogramBe careful though! The

height has to be perpendicular from the

base, just like the side of a rectangle!

Area Formulas

b.h

RhombusThe 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 cm2

27 in2Parallelogram

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?

b.h

2

TrapezoidBut now there is a problem.

What is wrong with the base?

Area Formulas

b.h2

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 1 base 2

base 2

The heights are the same, so no problem there.

(b1+ b2) h2

Practice!Trapezoid

11 m

3 m

5 m

Area Formulas

Answers

35 m2Trapezoid

11 m

3 m

5 m

Area Formulas

Summary so far...

bh

Summary so far...

bh

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bh

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bh bh

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bh bh2

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bh bh2

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bh bh2

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bh bh2

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bh bh2

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bh bh2

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bh bh2

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bh bh2

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bh bh2

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bh bh2

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bh bh2

(b1 + b2)h2

Summary so far...

bh bh2

(b1 + b2)h2

Summary so far...

bh bh2

(b1 + b2)h2

Summary so far...

bh bh2

(b1 + b2)h2

Summary so far...

bh bh2

(b1 + b2)h2

Summary so far...

bh bh2

(b1 + b2)h2

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

KiteNow we have to

determine the formula. What is

the area of a triangle formula again?

Area Formulas

KiteNow we have to determine the formula. What is the area of a triangle formula again?

bh2

Area Formulas

Fill in the blank. A kite is made up of __?__ triangles.

So it seems we should multiply the formula by 2.

Kite

bh2

*2 = bh

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.

bh2

. 2 = bh

Area Formulas

KiteLet’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 ft2Kite2 ft

10 ft

Area Formulas

Summary so far...

bh

Summary so far...

bh

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bh

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bh bh

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bh bh2

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bh bh2

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bh bh2

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bh bh2

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bh bh2

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bh bh2

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bh bh2

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bh bh2

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bh bh2

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bh bh2

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bh bh2

(b1 + b2)h2

Summary so far...

bh bh2

(b1 + b2)h2

Summary so far...

bh bh2

(b1 + b2)h2

Summary so far...

bh bh2

(b1 + b2)h2

Summary so far...

bh bh2

(b1 + b2)h2

Summary so far...

bh bh2

(b1 + b2)h2

Summary so far...

bh bh2

(b1 + b2)h2

Summary so far...

bh bh2

(b1 + b2)h2

Summary so far...

bh bh2

(b1 + b2)h2

Summary so far...

bh bh2

(b1 + b2)h2

Symmetry Line * Half the Other Diagonal

Final SummaryMake sure all your formulas are written

down!

bh bh2

(b1 + b2)h2

Symmetry Line * Half the Other Diagonal