geometry semester 2 notes
Geometry Notes Second Semester
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
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