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GMAT Quant > Geometry > Flashcards

Geometry Flashcards

1
Q

Hypotenuse = 10

A

Sides = 6 & 8

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2
Q

Hypotenuse = 15

A

Sides = 9 & 12

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3
Q

Hypotenuse = 17

A

Sides = 8 & 15

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4
Q

Hypotenuse = 26

A

Sides = 10 & 24

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5
Q

Sum of Any Two Sides of a Triangle

A

> 3rd side

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6
Q

Difference of Any Two Sides of a Triangle

A

< 3rd Side

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7
Q

Exterior Angle of a Triangle

A

A = C+D

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8
Q

30-60-90 Triangle

Ratio of Sides

A

** x : x(3)1/2 : 2x**

1 : (3)1/2 : 2

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9
Q

45-45-90 Triangle

Ratio of Sides

A

x : x: x(2)1/2

1 : 1 : (2)1/2

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10
Q

Sum of interior angles in a polygon with n sides

A

180 (n-2)

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11
Q

Measure of One Interior Angle

A
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12
Q

Volume of a Sphere

A
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13
Q

Volume of a Cylinder

A
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14
Q

Suface Area of a Cylinder

A

=
2(πr<span>2</span>) + 2(πrh)

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15
Q

Suface Area of a Sphere

A

=

4πr2

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16
Q

Area of Trapezoid

A

1/2 (sum of bases)(height)

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17
Q

Isoceles Trapezoid

A

A trapezoid in which the sides (not the bases) are of equal length

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18
Q

Area of an Equilateral

(shortcut formula )

A

Optimal use:

Given = one side of the triangle and you are asked to find area from that one side.

19
Q

Area of Reg. Hexagon

A
20
Q

Characteristics of a (regular) Hexagon

A
  1. six equal sides
  2. six equal angles
  3. Σ interior angles = 720°, each angle 120°
  4. six equilateral triangles formed by three diagonals
21
Q

Suplementary Angles

A

Form a straight line

&

= 180o

22
Q

Quadrilaterals

A

Parralellograms, Square, & Rectangles

23
Q

Characteristics of a Parallelogram

A
  1. Opposite angles are equal
  2. Any two consecutive angles are supplementary (= 180°)
  3. All rectangles
24
Q

Area of the Parallelogram

A
25
Q

Polygon(s)

A

A closed 2-D geometric figure composed of only straight lines.

Squares, rectangles, hexagons, rhombuses, etc.

26
Q

Polygon inscribed in a circle means?

A

The circle into arcs of equal length

27
Q

Exterior Angles of Any Polygon

A

=

360° (when taking one exterior angle at each vertex)

28
Q

Characteristics of a Square

A
  1. considered a “special” rectangle - rectangle with equal sides
  2. each diagonal divides the square into two equal 45-45-90 degree triangles
  3. all angles are equal
29
Q

Length of a Diagonal of a Square

A

= side * 21/2

“the length of one side times the square root of two”

30
Q

Suface Area of a Cube

A

= 6s2

31
Q

Diagonal of a cube

A

= s(31/2)

or

“side root three”

32
Q

Diagonal of a Rectangle

A

*But remember* diagonals of a rectangle do not auto make

congruent 30-60-90 triangles.

PAY ATTN to the givens!!

33
Q

Suface Area of Rectangular Solid

A

= 2(LW) + 2(LH) + 2(WH)

34
Q

Diagonal of Rectagular Solid

(aka Super Pythagorean Theorem)

A

d2 = l2 + w2 + h2

35
Q

Sum of Exterior Angles of any Polygon

A

= 360o

36
Q

Comparing two quadrilaterals with the same perimeter. Which quad has the greater area?

A

Square. Because it’s a “squared” calculation.

37
Q

A rectangle and square have the same area (fixed area),

which figure has a smaller perimeter?

A

The “rectangle” with the smallest (min.) perimeter

= a square

38
Q

Isoceles Triagle

A

= 2 sides are equal and two angles are equal

39
Q

Area of an Isosceles Right Triagle

A

=

(l1+ l2)/2

or

SHORTCUT !

L2/2

40
Q

If there are two quadrilaterals (a square & and a rectangle)

w/ the same perimeter, which of the two quads will have a larger area?

A

If the rectangle and square have the same perimeter, there are of the square will ALWAYS be larger.

Why?

Area of a square is a squared measure whereas the area of a rectangle is not.

41
Q

Equilateral Triangle inscribed in a Circle

A
  1. Triangle divides the the circle into three equal arcs
  2. Center if the equilateral triangle = center of circle
42
Q

Area of the shaded region

A

=

(area of entire figure) - (area of unshaded region)

43
Q

Perimeter of Shaded Region

A

=

(perimeter of entire region) + (perimeter of unshaded region)

44
Q

Area of circular ring

A

=

π [(radius2)2 - (radius1)2]

GMAT Quant (8 decks)

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