Geometry (Area & Pythagorus theorum)

Question 1

What is area

Answer 1

• 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

Question 2

What are the units for area

Answer 2

milimeters - mm^2
centimeters - cm^2
meters - m^2

Question 3

Formulas for area
rectangle -

Answer 3

rectangle - l x w

Question 4

Formulas for area
triangle -

Answer 4

triangle - (b x h)/2

Question 5

Formulas for area
parallelogram -

Answer 5

parallelogram - b x h

Question 6

Formulas for area
circle -

Answer 6

circle - π r^2

Question 7

Formulas for area
trapezia -

Answer 7

trapezia - ((a + b)/2) x h

Question 8

Pythagorus theorem

Answer 8

a^2 + b^2 = c^2

Question 9

What is the difference between area and surface area

Answer 9

• 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

Question 10

How can you find out surface area

Answer 10

1. Consider the net, or the way the 3d shape unfolds, and the different faces the shape might have
2. Use formula for the shape

Question 11

SA of hollow cylinder formula

Answer 11

2 π r h

Question 12

SA of open end cylinder (one side) formula

Answer 12

2 π r h +π r^2

Question 13

SA of solid cylinder formula

Answer 13

2 π r h + 2π r^2

Question 14

What is volume

Answer 14

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

Question 15

What are the conversions for volume units

Answer 15

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

Question 16

What is the formula for volume of a tapered solid, eg. cone, or pyramid

Answer 16

1/3 x Area of Base x Height

Question 17

Formula for volume of a sphere

Answer 17

V = 4/3 π r^3

Question 18

Formula for volume of a trapezia

Answer 18

((a+b)/2) x height x length

Question 19

What is equation of a line

Answer 19

An algebraic way to find all points on a line and whether points are on the line or not

Question 20

What is the gradient intercept form and what does it mean

Answer 20

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

Question 21

How do we calculate distance between points

Answer 21

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

Question 22

What is (x2, y2) and (x1, y1)

Answer 22

(x2, y2) is the rightmost point, and
(x1, y1) is the leftmost point

Question 23

What are the types of triangles

Answer 23

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

Question 24

How can we calculate the midpoint between two points

Answer 24

We can use the formula (x1+x2)/2, (y1+y2)/2 to calculate the midpoint