Geometry

Question 1

Hypotenuse = 10

Answer 1

Sides = 6 & 8

Question 2

Hypotenuse = 15

Answer 2

Sides = 9 & 12

Question 3

Hypotenuse = 17

Answer 3

Sides = 8 & 15

Question 4

Hypotenuse = 26

Answer 4

Sides = 10 & 24

Question 5

Sum of Any Two Sides of a Triangle

Answer 5

> 3rd side

Question 6

Difference of Any Two Sides of a Triangle

Answer 6

< 3rd Side

Question 7

Exterior Angle of a Triangle

Answer 7

A = C+D

Question 8

30-60-90 Triangle

Ratio of Sides

Answer 8

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

1 : (3)^1/2 : 2

Question 9

45-45-90 Triangle

Ratio of Sides

Answer 9

x : x: x(2)^1/2

1 : 1 : (2)^1/2

Question 10

Sum of interior angles in a polygon with n sides

Answer 10

180 (n-2)

Question 11

Measure of One Interior Angle

Answer 11

Question 12

Volume of a Sphere

Question 13

Volume of a Cylinder

Question 14

Suface Area of a Cylinder

Answer 14

=
2(πr^{<span>2</span>}) + 2(πrh)

Question 15

Suface Area of a Sphere

Answer 15

=

4πr²

Question 16

Area of Trapezoid

Answer 16

1/2 (sum of bases)(height)

Question 17

Isoceles Trapezoid

Answer 17

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

Question 18

Area of an Equilateral

(shortcut formula )

Answer 18

Optimal use:

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

Question 19

Area of Reg. Hexagon

Answer 19

Question 20

Characteristics of a (regular) Hexagon

Answer 20

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

Question 21

Suplementary Angles

Answer 21

Form a straight line

&

= 180^o

Question 22

Quadrilaterals

Answer 22

Parralellograms, Square, & Rectangles

Question 23

Characteristics of a Parallelogram

Answer 23

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

Question 24

Area of the Parallelogram

Answer 24

Question 25

Polygon(s)

Answer 25

A closed 2-D geometric figure composed of only straight lines. Squares, rectangles, hexagons, rhombuses, etc.

Question 26

Polygon inscribed in a circle means?

Answer 26

The circle into arcs of equal length

Question 27

Exterior Angles of Any Polygon

Answer 27

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

Question 28

Characteristics of a Square

Answer 28

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

Question 29

Length of a Diagonal of a Square

Answer 29

= side \* 2^1/2 "the length of one side ***times*** the square root of two"

Question 30

Suface Area of a Cube

Answer 30

= 6s²

Question 31

Diagonal of a cube

Answer 31

= s(3^1/2) or "side root three"

Question 32

Diagonal of a Rectangle

Answer 32

\*But remember\* diagonals of a rectangle **_do not_** auto make congruent 30-60-90 triangles. **PAY ATTN** to the givens!!

Question 33

Suface Area of Rectangular Solid

Answer 33

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

Question 34

Diagonal of Rectagular Solid | (aka Super Pythagorean Theorem)

Answer 34

d² = l² + w² + h²

Question 35

Sum of Exterior Angles of any Polygon

Answer 35

= 360^o

Question 36

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

Answer 36

Square. Because it's a "squared" calculation.

Question 37

A rectangle and square have the same area (fixed area), which figure has a smaller perimeter?

Answer 37

The "rectangle" with the smallest (min.) perimeter = **a square**

Question 38

Isoceles Triagle

Answer 38

= 2 sides are equal and two angles are equal

Question 39

Area of an Isosceles Right Triagle

Answer 39

= (*l₁ *+ *l₂*)/2 *or* **SHORTCUT !** L²/2

Question 40

If there are two quadrilaterals (a square & and a rectangle) w/ the same perimeter, which of the two quads will have a larger area?

Answer 40

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.

Question 41

Equilateral Triangle inscribed in a Circle

Answer 41

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

Question 42

Area of the shaded region

Answer 42

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

Question 43

Perimeter of Shaded Region

Answer 43

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

Question 44

Area of circular ring

Answer 44

= π [(radius₂)² - (radius₁)²]