SHAPEDRafael López

VERTICES, EDGES, FACES

CIRCLES

CDIAMETER

RADIUS

AREA: A= r2

CIRCUMFRANCE= C= d or C= 2 r

CongruencyC

A

B

F

ED

ABC DEF

FGHJKL - MNPQRS

K J

F

L H

G

R

S

Q N

M

P

Xcm

6 cm

4 cm

2 cm

6/4 = X/24x = 124x =124x/4 =12/4

NP/GH= RQ/ KJ

Cross Multiply

APPLICATIONS AND PROPORTION

X ft

6 ft

45 ft 3 ft

6/x= 3/453x= 2703x/ 3=270/ 3X=90

Mans height / poles height= Mans shadow/ poles shadow

CHANGING DIMENSIONS

A B4

2

6

3

PERIMETER: 2 (L) + 2 (W)Rectangle A: 2( 2) + 2 (W)= 12Rectangle B: 2 ( 6) + 2 ( W)= 18

AREA: L x WRectangle A: 4 x 2 = 8Rectangle B: 6 x 3 = 18

Sides: 4/6 =2/3

perimeters: 12/ 18= 2/3

Areas: 8/18 = 4/6 = (2/3) 2

Viewing solids from different perspectives

Front view

Top view

Side view

prism

B: ½ x BxHB: ½ (13) (14) B: 39in.2

V: B xHV: (39) (4)V: 156 in. 3

Volume= ( Area of one base) x (Height of the prism )

FORMULAS FOR VOLUME

Prism

Cube

Pyramid

Cylinder

Cone

B B x H

S3

1/3 B x H

r2h

1/3 r2h

B: area of baseH: Height of prism

S: length of one side

B: area of baseH: Height of pyramid

r : RadiusH: Height

r : RadiusH: Height

Volume of Sphere

V= 4/3 r3

V= 4/3 (3.14) (33) V= 113.04

3 cm

Classifying Solids

A prism is a solid formed by two congruent polygon bases connected by rectangular lateral faces. A prism is named with regard to the polygon basesA cylinder is a solid formed by two congruent circular bases

A pyramid is a solid formed by one polygon base. The lateral faces are triangles that meet at a vertex. A pyramid is named with regard to the polygon base.

A cone is a solid formed by one circular base with a vertex at the opposite end

Volume practice

B: ½ x BxHB: ½ (8) ( 30)B: ½ ( 240) B: 120

V: B x HV: 120 x 30V: 3600

V= r2hV= 3. 14 x (10 2)x 23V= 3.14 x 20 x 23V= 3.14 x 460V= 1444.4