Formulas…• They help us find the area.• They did not fall out of the sky!• In Exploration 10.7, you will develop the

formulas for the area of a triangle, rectangle, and parallelogram.

• Now, let’s develop the formula for the area of a trapezoid.

Area of Trapezoids• First method: draw a diagonal, and find

the area of 2 triangles.

Base 1

Base 2

Height

Area of Trapezoids• Method 2: make a 180˚ rotated image;

find the area, and cut it in half.

Base 1

Base 2

Height

Base 1

Base 2

Height

Area of a circle• If you like, read Exploration 10.8. It

explains in more detail why the area of a circle is πr2.

• Take any circle.

• Subdivide it into many congruentsectors--in this case,we made 16.

• Cut out each sector. Rearrange them.

• What shape does this remind you of?– What is the formula for finding the area of this shape? Find it!

Pythagorean Theorem • The most proved theorem ever--over

300 proofs! One was done by James Garfield, before he was president of the United States.

• If you have a right triangle with hypotenuse of length “c”, then

a2 + b2 = c2.

It looks like this!• a2 + b2 = c2.

But we use it like this.• Find the perimeter and area of this

triangle.

5 feet

x feet

13 feet

Other ways to make our life easy.

• Compare the circumference and area.

r

2r

Try this--find perimeter and area

13 “13 “

10 “

10 “

20 “

• P = tri + rect + sem13 + 13 + 10 + 20 + 10 + sem (.5 • 2π• 5)

• A = tri + rect + sem52 + x2 = 132

x = 12.5•10•12 + 20•10 + .5•π•52

13 “13 “

10 “

10 “

20 “

Try to find the shaded area• Assume the

trapezoidisisosceles.

24 cm

24 cm

38 cm--whole base7 cm

4 cm

• Area of trapezoid - area of parallelogram• Trap: .5 • 24 (24 + 38)• Para: 7 • 4• Did not need

PythagoreanTheorem!

24 cm

24 cm

38 cm--whole base7 cm

4 cm

Find the perimeter and area…

• If it looks right or congruent, it is.

• (1) (2)

9 in.9 in.

18 in.

18 in.

10 m

14 m4 m2

2.8 m

2 m

One• Perimeter

– Sides of largetriangle: 92 + 92 = x2

x = 12.712.7 + 12.7 + 12.7 + 12.7

+ 9 + 9 = 68.6 in.

• Area: Note that the largetriangle can be moved to make a rectangular figure.– 9 • 18 = 162 in.2

9 in.9 in.

18 in.

18 in.

Two• Perimeter:

– 10 + 10 + 2.8 + 2.8+ 2.8 + 2.8 + 2 + 2 =35.2 m

• Area:– Two trapezoids and a rectangle– (.5)(2)(10 + 14) + (.5)(2)(10 + 14) + 2 • 14– 84 m2

10 m

14 m4 m2

2.8 m

2 m