Measurement Project Concept Map

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Multiple Equations

par Jackie Lindquist

Hannah Froiland- Measurement

par Hannah Froiland

Rendering

par Mike Ton

Grade 10 Mathematics

par Kiana Roomes

Measurement Project Concept Map

Jasmine- Geometric Figures

Adam- Surface area, volume, pythagorean theorem

Kylie- Area and Perimeter

Area and Perimeter

Perimeter

SQUARE To find the peimeter of a square all you have to do is multiply what ever number is shown for the sides by four because all of the sides on a square are the same size.

CIRCLE To find the perimeter of a circle you use the formula Circumfrence= Pie*diameter or Circumfrence=Pie*Radius *radius

TRIANGLE To find the perimeter of a triangle you simply add up all of the sides if all of the sides lengths are given. If on the other hand the triangle has a missing sign you then use the pythagorean Theorem which looks like this A2+B2=C2

Area

CIRCLE To find the area of a circle you use the formula Area=pie*diameter or if you just have the radius then the formula is Area=pie*radius*radius

RECTANGLE To find the area if a rectangle you multiply length times width

TRAPIZOID To find the area of a trapizoid you take the sum of the bases and then multiply by the height of the trapizoid, and then you divivde the number by two. Viola!

Volume of Polyhedrons

How to find the volume of Polyhedrons

The first thing we have to do in order to solve this problem is to fing the area of the base. To do that we need to multiply Lxh. 6x4=24. 24 is now B. Remember the equation to find the volume of pyramids is (1/3)xBxh=V. we can now plug in B and h and proceed to find the volume. (1/3)x24x5 is what our equation looks like now. multiplying that out gives us 40. 40 u^3 is the volume of this pyramid

For This Example h=5, w=4, L=6

Pyramids: One third of the area of the base times the height. Equation: (1/3) x B x h B=Area of base h=height

Prisms: The area of the base multiplied by the height. Equation: B x h B=Area of base h=height

Volume is the measure of the space inside a three-dimentional figure.

Main topic

Surface Area Polyhedrons

For this example the height(h) is 4, the length(L) is 5 and the width(w) is 3.

The first thing that needs to be done is finding the area and perimeter of this shape's base. The perimeter of the base is 2(5) + 2(3)= 16 = p The Area of the base is 5 x 3 = 15 = B Remember our equation for finding the surface area of prisms is 2B + ph. Since we know all the variables we can plug them in now. 2(15) + 16(4) - 30 + 64 - 94 u^2 = Surface area

Surface Area Equations

Key: B=Area of th base, p=Perimeter of the base, h=height

Pyramid: B + (1/2)ph

Prism: 2B + ph

Polyhedrons are the 3-D shapes that are made up of several flat faces. Some Examples are in the Pyramids and Prisms section.

Surface area: The total area of the surface of a three-dimensional object

Geometric Figures

Prisms and Pyramids

Pyramids

-a simple closed surface given by a polygon (its base) and a point not in the plane of the polygon, called its apex or vertex.

-the pyrmaid is the union of the base with all of the triangular faces that rise from the base edges to the apex.

*Polyhedron determined by polygon ( example. rectangular base = rectangular pyramid)

*points not in the plane

*does not have two congruent faces

Prisms

Prism - a simple closed surface that consists of two congruent polygons which are in parallel planes (bases) and the lateral faces joining the bases, which are parallelograms

* Two congruent faces (the bases)

*Have to be parallel planes

*other faces are bound by parallelograms

two dimensionsal vs. three dimensional:

- a prism is three dimensional and belongs on two planes in space, whereas a two dimensional figure only has one plane.

oblique prism

the edges between the bases are not perpendicular to the plane of the base

right prism

if the lateral faces of a prism are all rectangles

Classification of Polygons

How to find the measures of a Polygon

in a regular n-gon ( n = number of sides)

(x = multiply)

- each interior angles has a measure (n - 2) x 180 degrees/ n

- each exterior angle has measure 360 degrees / n

- each central angle has measure 360 degrees / n

Regular Polygons

polygons that include some degree of symmetry

Regular polygon- a convex polygon that is both equiangular and equilateral

equilateral- a polygon with all congruent sides

equiangular- a polygon with all equal angles

Circles

- a circle is a two- dimensional shape (mathisfun.com)

-the set of all points that are an equal distance from the center

Types of Quadrilaterals

A quadilateral means "four sides" so is any four sided shape

Types of Triangles

Classification by side lengths

Isosceles

When two sides have the same length

Equilateral

all three sides have the same length and are congruent

Scalene

all three sides have a different length

( no two sides are congruent)

Classification by angle measure

Obtuse

if one angle has a measure more than 90 degrees.

Right

one angle is a right angle (90 degrees)

Acute

all three interior angles are less than 90 degrees

Angles

Definition of an Angle: A shape, formed by two lines or rays diverging from a common point known as the vertex.

( www.mathopenref.com )

< = angle

The sum of angle measures in Triangles

the sum of all angles in a triangle is 180 degrees.

Angle Measure

- the number of degrees of turn to rotate about the vertex (middle point)

-Measured in degrees

Classification of angles

Corresponding angles

corresponding angles property:

- when two parallel lines are cut by a transversal (intersecting line), then their corresponding angles have the same measure

-if two lines in the plane are intersected by a transversal and some pair of their corresponding angles has the same measures, then the lines are parallel

Alternate-exterior-Angles

The pair of angles on the opposite sides of the transversal but outside the two lines (mathisfun.com).

Alternate- Interior- Angles

The pair of sides on the opposite of the transversal, but inside the two lines (mathisfun.com).

Vertical angles

- vertical angles are congruent

Two nonadjacent angles formed by two intersecting lines

Congruent angles

When two angles are congruent, they are also equal !

when two angles have the same exact measure

Complimentary angles

when the sum of two angles measure 90 degrees.

Supplementary angles

when the sum of two angles measure 180 degrees

Pythagorean Theorem

To solve for C: Plug in the numbers you can into the equation A^2 + B^2 = C^2. Since we know A and B we can plug those in, gic=ving you 5^2 + 12^2 = C^. This can be simplified to be 169 = C^2. Taking the square root of both 169 and C^2 you are left with the answer: C = 18.

For this example lets suppose that A=5 and B=12.

Pythagorean Theorem: a^2 + b^2 = c^2

-The Pythagorean Theorem is an equation devised to find the slope opposite the 90 degree angle or right Triangles. A^2 + B^2 = C^2 is the relationship between the sides of the triangle in regard to length.

-This equation only works on right triangles

- A is the height, B is the width and C is the length of the slope.

The Pythagorean Theorem Is an equation devided to find the length of the slope opposite the 90 degree angle in right triangles. A^2 + B^2 = C^2 is the relationship in length between the sides of the triangle.