# geometry semester 2 notes

I.Area, Surface Area and Volume & Circumference

Circumference is the linear distance around the outside of a circular object. •C = π • d or π • 2r.

•d = diamater or (radius • 2)

•r = radius

II.Perimeter

Perimeter is the distance around a figure.

* It is found by adding the lengths of all the sides.

* Finding perimeter on the coordinate plane may require the use of the distance formula: (2 x width) + (2 x height) III.Regular Polygon

•A regular polygon is a polygon that is equiangular and equilateral. • A = ½ ap

• a = Apothem is distance from the center of a polygon to one of its sides. • p = ns

• n = number of sides

• s = length of each side

IV.Area of a Regular Polygon

Area = ½ (p • a)

p = perimeter

a = apothem

V.Square

•Area of a square = a*a

a = length of side

VI.Triangle

•Area of a triangle= ½ b*h

b = base

h = vertical height

VII.Parallelogram

•Area of a parallelogram = b *h

b = base

h = vertical height

VIII.Trapezoid

• Area of a trapezoid = ½ (a + b) • h

a = 1st base

b = 2nd base

h = vertical height

IX.Rectangle

•Area of a rectangle = b • h

b = base

h = height

X. Circle

•Area of a circle = πr • r

r = radius

radius = diameter / 2

XI. Prism

A prism is a polyhedron with two congruent, parallel faces, called bases. The other faces are lateral faces. An altitude of a prism is a perpendicular segment that joins the planes of the basses. The height of a prism is the length of an altitude. In a right prism, the lateral faces are rectangles and a lateral edge is an altitude. In an oblique prism, some or all of the lateral faces are nonrectangular. XII. Lateral Area

Lateral area of a prism is the sum of the areas of all the lateral faces. •L.A. = ph

p = perimeter of the base

h = height of the prism

XIII. Surface Area

Surface area of a prism is the sum of the lateral area and the area of the two bases. •S.A. = L.A. + 2B

B = area of the base

XIV. Surface Area Pyramid

•Surface Area = L.A. + B

B = base area

Lateral Area = ½ pl

p = perimeter of base

l = slant height

XV. Cones

A cone is a 3D figure with one circular base and one vertex. •Surface Area = L.A. + B

B = base area

Lateral Area = π • r • l

r = radius

l = slant height

XVI. Sphere

•Surface area = 4π (r • r)

r = radius

XVII. Volume

Prisms

Volume = A • L

A = area of base

L = length of prism

Cylinders

Volume = π (r • r) h

r = radius of base circle

h = height of cylinder

Pyramids

Volume = 1/3 (Ah)

A = area of base

h = height

Square Pyramids

Volume = 1/3 (l • l) h

l = length of side of base

h = height

Cones

Volume = 1/3 π (r • r) h

r = radius*

h = height

Sphere

Volume = 4/3 π (r • r • r)

r = radius

XVIII. Triangles

•Types of Triangles

45 - 45 - 90 Triangle

The height and base of a 45 - 45 - 90 Triangle are equal. The hypotenuse is the height or base multiplied by radical 2. 30 - 60 - 90 Triangle

The side across from the 30 degree angle is x. The hypotenuse is 2x. The side across from the 60 degree angle is x multiplied by radical 3. Isosceles Triangles

An Isosceles ∆ is a ∆ with at least 2 congruent sides. Isosceles Triangle Theorem

If two sides of a triangle are congruent, then the angles opposite to those sides are congruent. Converse of Isosceles Triangle Theorem

If two angles of a triangle are congruent, then the sides opposite to the angles are congruent. Equilateral Triangles

An Equilateral ∆ is a ∆ in which all three sides are equal. All three internal angles are also congruent to each other and are each 60°. Scalene Triangles

A Scalene ∆ is a ∆ in which all sides are not equal.

Congruency Postulates & Theorems

•Postulate

If three sides of one triangle are congruent to three sides of another triangle, then these two triangles are congruent. •SAS Postulate

If two...

Please join StudyMode to read the full document