Geometry (Area & Pythagorus theorum) Flashcards
What is area
- Area is the space taken up by a 2d space
- Calculated in square units
- Each 2d shape has its own area formula
- It is the number of 2d square units that will fit inside of a 2d shape
What are the units for area
milimeters - mm^2
centimeters - cm^2
meters - m^2
Formulas for area
rectangle -
rectangle - l x w
Formulas for area
triangle -
triangle - (b x h)/2
Formulas for area
parallelogram -
parallelogram - b x h
Formulas for area
circle -
circle - π r^2
Formulas for area
trapezia -
trapezia - ((a + b)/2) x h
Pythagorus theorem
a^2 + b^2 = c^2
What is the difference between area and surface area
- Area is the space taken up by a 2d shape
- Surface area is the area of all the combined areas of the faces of a 3d shape
How can you find out surface area
- Consider the net, or the way the 3d shape unfolds, and the different faces the shape might have
- Use formula for the shape
SA of hollow cylinder formula
2 π r h
SA of open end cylinder (one side) formula
2 π r h +π r^2
SA of solid cylinder formula
2 π r h + 2π r^2
What is volume
The space taken by a 3d shape - calculated in cubed units
We can convert volume units to capcity units, which calculates how much a 3d shape can hold
What are the conversions for volume units
1 cm = 10 mm, so we can see that
1 cm^3 = 10mm.10mm.10mm = 1000mm^3
Similarly, 1 m^3 = 100 cm x 100 xm x 100 cm = 1,000,000
What is the formula for volume of a tapered solid, eg. cone, or pyramid
1/3 x Area of Base x Height
Formula for volume of a sphere
V = 4/3 π r^3
Formula for volume of a trapezia
((a+b)/2) x height x length
What is equation of a line
An algebraic way to find all points on a line and whether points are on the line or not
What is the gradient intercept form and what does it mean
y = mx + c (quick way to identify and graph lines)
m = gradient of slope
c = where the line crosse the y-axis, in other words, y intercept
How do we calculate distance between points
We can use Pythagorean Theorem to calculate unknown lengths of right angle triangles
Pythagorean Theorem a^2+b^2 = c^2
We can use the formula
√(x2 - x 1)^2 + (y2 - y1)^2 to calculate the distance
*This is always with a right angle triangle
What is (x2, y2) and (x1, y1)
(x2, y2) is the rightmost point, and
(x1, y1) is the leftmost point
What are the types of triangles
Equilateral = all the sides are the same length
Isosceles = two of the sides are the same length
Scalene = none of the sides are the same length
Scaley, so weird, so none are same
How can we calculate the midpoint between two points
We can use the formula (x1+x2)/2, (y1+y2)/2 to calculate the midpoint
