Geometry

Question 1

Triangles Perimeter

Answer 1

P = A + B + C

Question 2

Triangle Area

Answer 2

A = (B×H) ÷ 2

Question 3

Specific triangles

Answer 3

30-60-30 = 1:sqrt(3):2 - 45-45-90 = 1:1:sqrt(2)

Question 4

Square properties

Answer 4

All opposites sides are parallel and have the same length. All angles are 90°. Diagonal have the same length, intersect at 90° and bisect each other. Interior angles add up to 360°.

Question 5

Square area

Answer 5

A = s2

Question 6

Square perimeter

Answer 6

P = 4s

Question 7

Square key shapes

Answer 7

Diagonals create two 45-45-90 isoceles right triangles.

Question 8

Rectangle properties

Answer 8

All opposites sides are parallel. Opposite sides are the same length. All angles are 90°. Diagonals are the same length and bisect each other. Interior angles add up to 360°.

Question 9

Rectangle area

Answer 9

A = l × w

Question 10

Rectangle perimeter

Answer 10

P = 2l + 2w

Question 11

Rectangle key shapes

Answer 11

Diagonals create 2 right triangles.

Question 12

Parallelogram properties

Answer 12

All opposites sides are parallel. Opposite sides are the same length. Opposite angles are equal. Diagonals bisect each other. Interior angles add up to 360°.

Question 13

Parallelogram area

Answer 13

A = b × h

Question 14

Parallelogram perimeter

Answer 14

P = 2a + 2b

Question 15

Parallelogram key shapes

Answer 15

Right triangle needed to find the height.

Question 16

Trapezoid properties

Answer 16

2 sides are parallel. Interior angles add up to 360°.

Question 17

Trapezoid area

Answer 17

A = 1/2 (b+c)h with b and c the length of the parallel sides.

Question 18

Trapezoid perimeter

Answer 18

P = a + b + c + d

Question 19

Trapezoid key shapes

Answer 19

Right triangle needed to find the height.

Question 20

Sum of angles of a polygon

Answer 20

SoA = (n-2)×180 (with n the number of sides)

Question 21

Circle area

Answer 21

A = πr^2

Question 22

Circle circumference

Answer 22

C = 2πr

Question 23

Circle arc length

Answer 23

AL = 2πr ( x/360 ) with x the central angle measure

Question 24

Circle - Similar inscribed angles

Answer 24

All inscribed angles that extend to the same arc or same two points on a circle are equal.

Question 25

Circle - Central angle x vs. inscribed angle y

Answer 25

Any central angle that extends to the same arc or same two points on a circle as does an inscribed angle is twice the size of the inscribed angle. x = 2y

Question 26

Circle - Triangles inscribed in a semicircle

Answer 26

Any triangle inscribed in a semicircle with the circle diameter as longer side is always a right triangle.

Question 27

3D figures - Volume

Answer 27

V = (area of 2-D surface)×h

Question 28

Cube volume

Answer 28

V = s3

Question 29

Cube surface area

Answer 29

SA = 6s2

Question 30

Cube longest length within

Answer 30

L = sqrt(3s^2)

Question 31

Rectangular solid volume

Answer 31

V = lwh

Question 32

Rectangular solid surface area

Answer 32

SA = 2lw + 2lh + 2hw

Question 33

Rectangular solid longest length within

Answer 33

L = sqrt( l^2 + w^2 + h^2 )

Question 34

Cylinder volume

Answer 34

V = π×r^2×h

Question 35

Cylinder surface area

Answer 35

SA = 2(πr^2) + 2πrh

Question 36

Cylinder longest length within

Answer 36

L = sqrt(4r^2 + h^2)

Question 37

Cylinder longest length within

Answer 37

L = sqrt(4r^2 + h^2)

Question 38

Cylinder longest length within

Answer 38

L = sqrt(4r^2 + h^2)

Question 39

Sphere volume

Answer 39

V = (4/3)πr^3

Question 40

Sphere surface area

Answer 40

SA = 4πr^2

Question 41

Sphere longest length within

Answer 41

L = 2r

Question 42

Slope intercept formula

Answer 42

y = mx + b with m the slope, b the y-intercept and (-b/m) the x-intercept.

Question 43

Slope of a line

Answer 43

Δy / Δx = (y2 - y1) / (x2 - x1)

Question 44

x- and y-intercepts

Answer 44

1 - Use y = mx + b formula. 2 - Set x equal to 0 to find the y-intercept. Set y equal to 0 to find the x-intercept.

Question 45

Calculating intersections of two lines

Answer 45

Set both equations equal to each other and resolve. (l1) : y=ax+b ; (l2) : y=mx+p –> ax+b=mx+p

Question 46

Distance between any two points

Answer 46

(p1) : (x1, y1) ; (p2) : (x2, y2) –> d(p1, p2) = sqrt( (Δx)^2 + (Δy)^2 ) = sqrt( (x1-x2)^2 + (y1-y2)^2 )

Question 47

Midpoint formula

Answer 47

(p1) : (x1, y1) ; (p2) : (x2, y2) –> Midpoint = ( (x1+x2)/2, (y1+y2)/2 )