Unit 8 Math test: Area/SA/Perimeter/etc.

Circle definition

A set of points in a plane at a given distance (equidistant) from a given point

Center (of a circle)

The center point

Radius

Distance from the center to a point on the circle

Central angle

An angle in the circle made up of two radii

Chord

A segment whose endpoints lie on a circle

Diameter

• 2 x radius

• A chord that contains the center of the circle

Circumference

The distance around a circle

Arc

A portion of the circles circumference

Area (of a circle)

The amount of space inside the circle

Sector

A portion of the circle

Secant

Any line that contains a chord (cuts through the circle)

Tangent

A line that intersects a circle at only one point

Circumference formula

2πr

Circle area formula

πr²

Arc measure

Will always be in degrees (degrees of the angle the arc involves)

Arc length (distance)

• Will always be in units

• A portion of the circumference of a circle

Arc length formula

2πr • x/360

Which equation (arc length vs. sector area) involves the circumference formula?

Arc length

Which equation (arc length vs. sector area) involves the area formula?

Sector area

Sector

Portion of a circle created by two radii

Area of a sector

Total area of a sector of a circle

Sector area formula

πr² • x/360

True or False: Arcs can have the same degree measure but different arc lengths

True

All arcs combined =

360˚

Central Angle

• Formed at the center of a circle due to the intersection of any two radii within the circle

• Always equal to the arc

Inscribed Angle

• An angle whose vertex lies on a circle and whose sides contain chords of the circle

• Arc = 2x angle

How do we name pyramids?

• Named after their bases

• Etc. triangular pyramid with a triangular base

What does polyhedra mean

Many sides

What are some polyhedra shape examples?

Prisms and pyramids

What are some non-polyhedra shape examples?

Cylinders, cones, and spheres

What does h stand for

Height

What does v stand for

Volume

What does capital B stand for

AREA of base

Lateral faces

Parallelograms formed by connecting the corresponding vertices of the bases

Lateral edges

The segments connecting the vertices

Lateral Area

• LA

• The sum of the area of the polyhedra's faces

Surface Area

• SA

• The total area of every surface on the 3-D shape

What is a cone?

A cone has a circular base with a vertex that is not in the same plane as the base

Lateral area of a cone formula

πrl

Surface area of a cone formula

πr² + πrl

What is a pyramid

A polyhedron with a polygon base (which names the type of pyramid) and the lateral faces are triangles with a common vertex

Lateral area of a pyramid formula

½ lp

Surface area of a pyramid formula

½ lp + B

What does l (lowercase L) stand for?

Slant height

What does p stand for?

Perimeter of base

Slant Height

• The height of a lateral face of a regular pyramid or cone

• Slant height is the hypotenuse of the right triangle with the height as one leg. The other leg is the radius in a cone or half of the length of the base in a pyramid.

Lateral Edge

The lateral edge is the hypotenuse of a right triangle where the slant height and half the base are legs in a pyramid

Inscribed Angles Theorem

If two inscribed angles of a circle intercepts the same arc then the inscribed angles are congruent

Sphere

• A set of equidistant points in space from a given point

• 3-D

Hemisphere

½ sphere

Surface area formula for spheres

4πr²

Volume formula for spheres

4/3πr³

Nets

A 2-D shape that can be folded together to form a 3-D shape; it represents the surface area of that solid

What two things make figures similar

• Corresponding sides are proportional

• Corresponding angles are congruent

What is the formula for the area of trapezoids?

A = ½ h( b₁+b₂ )

What is the formula for the area of rhombuses?

A = ½ d₁d₂

What is the formula for the area of kites?

A = ½ d₁d₂