Date post: | 04-Jan-2016 |
Category: |
Documents |
Upload: | augustine-dorsey |
View: | 224 times |
Download: | 3 times |
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