Chapter 9 and 10Journal

Marcela Janssen

areas

AreasSquare

base x height

Rectanglebase x height

Trianglebase x height 2

Parallelogram base x height

Trapezoid(base1 x base2)h 2

Kite(½ diagonal2) diagonal 1

Rhombus (½ diagonal2) diagonal 1

Any polygon with any # of sidesArea = (½ sa) n

Shape Formula Mis,

Square base x height

Rectangle base x height

Triangle base x height 2

Parallelogram

base x height

Trapezoid (base1 x base2)h 2

Kite (½ diagonal2) diagonal 1

Rhombus (½ diagonal2) diagonal 1

Any polygon with any # of sides

Area = (½ sa) n Sidesapothemn # of sides

Apothem ½ sides

tan 180/n

½ stan c/8

Examples

Area 9m 9m x 3m

27m2

3m

6mm 6mm x 4mm4mm 2 24/2 = 12mm2

Composite figures

Composite figuresComposite Figure:A plane figure made up of triangles,

rectangles, trapezoids, circles, or other simple shapes or a three dimensional-figure made up of prisms, cones, pyramids, cylinders and other simple three-dimensional figures.

Tridimensional composite figure

Plane figure

To find the area of a composite figure:

1. Divide tha figure into simple shapes

2. Find the areas of the simple shapes

3. Add all of the areas of the simple shapes to get the area of the whole composite figure

Example

2 cm

1 cm

12 cm

I

l

l

7 cm

(10 x 6)2 2120 260 cm

6cm

12x 224

60 + 2484 cm 2

Areas of circles

Areas of CirclesTo find the area of a circle just

use the equation:Area = π r 2

SOLIDS

Solids

A solid is a three-dimensional figure.

Sphere Triangular prism Rectangular ppyramid

PRISM

Prisms

Prism: is formed by 2 ll congruent polygonal faces called bases by faces that are parallelogram.

Difference bewteen a prism and a pyramid:Prism Has 2 bases

Pyramid Has 1 base

What does it look like?

To find the surface area of a prism:Surface Area = (perimeter of base)

L + 2(Area of base) Example: Surface A. = (16m) 7 + 2(24m2)

112 + 48 160 m2

A net is a diagram of the surfaces of a tridimensiitional object,

AREA OF CYLINDER

Cylinders

Is formed by two parallel congruent circular bases and a curved surface that connects the bases.

To find the surface area:Surface Area = 2(π r 2) + (2π r)h

Examples

AREA OF PYRAMID

NOT EXAMPLES

Pyramid

To find the total surface area:½ pl + b

L= lenght of the lateral face

P= perimeter opf the base

A= area of the base

AREA OF CONE

NOT EXAMPLES

Cone

To find the surface area of a cone:π r√r2 +h2

R= radius

H = height

AREA OF CUBE

Cube

A cube is a square prism with 6 congruent faces.

To find the surface area:6 a 2

A = lenght of edges

Example 1

Surface Area = 6(5 in)2 = 6(25) = 150 in2

Example 2

Given that the height of a cube is 5 ft 3 in what is the surface area that it has?

Surface Area = 6(5 ft 3 in)2 = 6(63 in)

= 6(63) = 378 in2

= 31.5 ft2

Example 3

How much is the surface area of this rubiks cube?

Surface Area = 6(8 in)2

= 6(64)

= 384 in2

CAVALIERI’S PRINCIPLE

Cavalieri’s PrincipleIf two three-dimensional figures

have the same base area, and same height, they will have the same volume.

VOLUMES

Volume PrismCylinderπ r2

Pyramid1/3 bhCone1/3 π r2 h

SPHERES

Spheres

Sphere: A tridimensional solid created by all points equidistant (radius) from the center point.

Hemisphere: Half of a sphereGreat Circle: Any line drawn aroud

the sphere that cuts it into two hemisphere (equator)

Surface area of a sphere:4 π r2

Example: r= 8.5 4π 8.52

4π 17

Volume of a sphere:4/3 π r3

How many water is needed to fill this sphere with water with a radius of 8.5?

4/3 π r3

4/3 π 8.53

86 mm

TO BE GRADED:SPHERESPRISMSAREA OF A CUBE