Areas + Measures

Cube

• Surface Area=

6e²

Cylinder

• Volume=

πr²h

(area of base)(Height)

Cube

• Volume=

e³

(l x w x h)

Rectangular solid

• Surface Area=

2lw + 2lh + 2hw

(sum of areas of faces)

Areas of Shaded Regions

• SQUARES:

  • Length of a side=

√area

Rectangular solid

• Volume=

lwh

(area of base)(h)

Areas of Shaded Regions

• Approach #2:

• Find area of the WHOLE figure

• Find areas of UNSHADED regions

• Subtract those from the whole area

Areas of Shaded Regions

• SQUARES:

  • Area of a square=

(Length of a side)²

Areas of Shaded Regions

• Approach #1:

• Break area of shaded region into smaller pieces

• Find areas of pieces

• Add areas together

Triangle inscribed in a semicircle where 1 side coincides w/ diameter of semicircle

• Triangle -

a right triangle

Polygon INSCRIBED in a circle=

All vericies of polygon lie on the circle

Polygon CIRCUMSCRIBED by a circle:

All sides of polygon are tangent to the circle

Circles

• Longest chord=

Diameter

Circles

• Tangent=

Line perpendicular to the radius

Circle

• Radius=

2r = d

To find the length of a line NOT parrallel to an axis:

• Make line segment the HYPOTENUSE

• Draw lengths of legs parrallel to the axes

• Find lengths of the legs

• Use Pythagorean Theorum (a² + b² = c² )

Circle

• Diameter=

d = 2r

Cylinder

• Lateral Surface Area=

2πrh

(circumfrence of base)(h)

Cylinder

• Total Surface Area=

2πr² + 2πrh

(areas of circular ends + lateral surface area)

Triangle

• Area=

½ (base)(height)

Parrallelogram

• Area=

A = bh

Square

• Area=

S²

(Side)²

Square

• Perimeter=

4(Side)

Rectangle

• Area=

lw

Rectangle

• Perimeter=

2( l + w)

Circle

• Area of a Sector=

n/360 x πr²

(n = degree of central angle)

Circle

• Arc Length=

n/360 × 2πr

(n = degree of central angle)

Circle

• Circumference=

C= πd or C= 2πr

Circle

• π =

3.14 → C/d

(Circumference / diameter)