GeometryMarch 17 & 18

College Readiness Standards:

•distinguish between area and perimeter, and find the area or perimeter when all relevant dimensions are given

Objectives

• All students will be able to find the perimeter of a polygon.

• Most students will be able find the area of a polygon.

• Some students will be able to apply the area and perimeter of polygons concept within a word problem

Agenda

• Bell ringer 10min/ Review 5 min

• Guide Practice word Problem 20min

• Word Problems for Polygons 20min

• Clean Up 5min

Bell Ringer 10min

Simplify the following expressions:

1. ax + x – 2ax + 4a2

2. 5x + x2 – y2 + xy2 – 10 + x +3x2

3. 10x2 + x -3

4. -3x3 – 8x3

Recap of 2-D Polygons

Shape P/C Area

• Square 2w + 2l l *w or s2

• Triangle a + b + c ½ b * h

• Circle 2πr or πd πr2

Standardized Prep Question

Davina has 38 inches of cording to frame a photograph in her scrapbook.

Which of these shapes would use most or all of the cording and enclose the largest area?

A right triangle with each leg about 9 inches long

B circle with a radius of about 6 inches

C rectangle with a length of 10.5 inches and a width of 7.5 inches

D square with a side length of 8.5 inches

Chart

• Class will organize results by making answer chart

Area and Perimeter of Triangle

Use the Pythagorean Theorem to find the length of the hypotenuse.

c2 = a2 + b2 Pythagorean Theorem

c2 = 92 + 92or 162 a = 9, b = 9

c = or about 12.7in. Simplify.

 

P = a + b + c Perimeter of a triangle

= 9 + 9 + 12.7 Substitution

= 30.7 in. Simplify.

 

A = ½bh Area of a triangle

= (9)(9) b = 9, h = 9

= 40.5 in2 Simplify.

Area and Perimeter of Circle

Circle

 

C = 2r

= 2(6)

37.7 in.

 

A = r2

= (6)2

113.1 in.2

Area and Perimeter of Rectangle

Rectangle

P = 2ℓ + 2w

= 2(10.5) + 2(7.5)

= 36 in.

 

A = ℓw

= (10.5)(7.5)

= 18.75 in.2

Area and Perimeter of Square

P = 4s

= 4(8.5)

= 34 in.

 

A = s2

= (8.5)2

= 72.25 in.2

Conclusion

• The shape that uses most of the cording and encloses the largest area is the circle. The answer is A.

Create your own problem

• Exit Ticket

• Please create two problems using area or perimeter with one of our polygons.

• Remember to create a problem, there needs to be one unknown value

Extra credit

• There is a square with a distance of 8.49 diagonally from corner to corner. What is the area of the square?

• Hint: 8.49 ≅√72

Algebraic Operations

Trapezoid