Welcome to Geometry!

Learning Target:

I will calculate the area of ANY regular polygon!

Welcome to Geometry!1. Sit in your assigned seat.2. Write down your learning target. 3. Silently start your warm-up for today.

(An SAT problem! )

Two sides of an isosceles triangle are 20 and 30. What is the difference of the largest and the smallest possible perimeters?

1. Sit in your assigned seat.2. Write down your learning target. 3. Silently work on your warm-up.

Learning Target:

You have 5 minutes

1. Sit in your assigned seat.2. Write down your learning target. 3. Silently work on your warm-up.

You have 4 minutes

You have 3 minutes

1. Sit in your assigned seat.2. Write down your learning target. 3. Silently work on your warm-up.

You have 2 minutes

1. Sit in your assigned seat.2. Write down your learning target. 3. Silently work on your warm-up.

You have 1 minutes

1. Sit in your assigned seat.2. Write down your learning target. 3. Silently work on your warm-up.

Time’s Up!1. Pencils Down2. Body Forward

3. Eyes on Ms. Chui4. Mouth Closed

Ready for Success!Learning

Target: I will calculate the area of ANY regular polygon!

FLO meetings today:

BlueStamp Engineering Houston Engineering

Thursday, Feb 20th (Lunch at 12:00, After School at 4:30)

G.R.A.D.E. The University of Houston Engineering

Thursday, Feb 20th (Lunch at 12:00, After School at 4:30)

Deadline to apply: March 7th, 2014

INTERESTED??

Go to the CCC during lunch and/or after

school!

If you’re applying to programs &

need help with essays, don’t be afraid to

ask!

Yesterday…•Naviance Quiz on Edmodo•Please complete!!

•Can’t log in to Naviance? Email Ms. Doan

Today’s objective…• How would I find the area of this shape??

Use what we have learned to come up with some ideas.

The method we are learning today works for ANY regular polygon

X out the NON polygons!

X out the NON polygons!

X XX X X

Polygon definition: ____________________________________

Closed figure with straight sides

X out the IRREGULAR polygons!

X X XX X X

All sides and all angles the same

Regular polygon definition: ____________________________________

Switch

Review: How do you find the area of a rectangle?•A = bh or A = lw

Parallelograms are awesome

What would happen if I cut a triangle off of one end of the parallelogram and translated it to the other side?

What shape have we formed?

So how do you find the area?

A = lw or A = bh

Review: How do you find the area of a triangle?•A = ½ bh or A = bh/2

Review: How do you find the area of a circle?

•A = π r 2

How about a pentagon?What if we cut the pentagon into congruent triangles?If you know the height of the triangle,

you can find the area.

So does the formula from the formula chart for a regular polygon make sense?

A = ½ aP

(A = ½ the apothem times the Perimeter)

The height of one of those triangles would be perpendicular to the base and go right to the middle of the pentagon.

That’s what we call the “apothem” of the polygon

18.2 cm

If it is a regular pentagon, it’s easy.

12.5 cm A = ½ (b) (h) so A = ½ (18.2) (12.5)

The area of one of the triangles is 113.75 cm2

How many triangles are there?

12

a P_apothem perimeter

Add up all the sides!!

center regular polygonmidpoint

perpendicular(90°)

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The apothem is a PERPENDICULAR BISECTOR!

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CORNER/VERTICES SIDE

Radius or apothem?

Radius or apothem?

Radius or apothem?

Radius or apothem?

Now for an example problem:

A = ½ a P5.1

P = 7.5 * 5

P = 37.5

37.5

A = ½ a PA = ½ * 5.1 * 37.5

A = 95.625A = 95.63 units2

≈2.31

Practice makes Permanent!

• Finished early? • Go to

mschuigeometry.weebly.com• Click on Lessons• Scroll down to Thursday• Click on Extended Practice• Read the first page

Your HW is on the website!