Geometry Flashcards
What is the area of a rectangular field that is 25 feet long, 12 feet wide?
300 ft2 (units are square feet)
A = LW (Area = Length*Width)
Multiplying by 25 –> can think of it as 12 quarters is 3 dollars (300 cents).
What is the perimeter of a rectangle with length 19 and width 13?
64
P = 2(L+W) = 2*32 =64
or, 2L+2W, but this is 3 steps to calculate instead of 2
If a rectangle has an area of 100, what is the minimum perimeter?
The minimum perimeter for rectangle of a fixed area is a square shape.
Take square root of 100 –> 10 on each side of square
4*10 = 40
What is the formula for volume of a rectangular solid? (also known as a “rectangular prism”)
V = LWH (length*width*height)
If 2 lines are perpendicular, what does that mean?
They form a right angle.
It is indicated by the square symbol below (dotted gray line)
What is the pythagorean theorem?
What is the formula for the diagonal of a rectangular solid?
This is called the Deluxe Pythagorean Theorem
(Pythagorean Theorem applied to 3 dimensions)
3
32 +42 = 52
The 3-4-5 triangle is good to memorize.
Other right triangles can have the same ratio: 6-8-10, 9-12-15, etc.
What is true about an isocoles triangle?
How do we draw it and identify the properties?
If 2 sides are equal, the 2 angles opposite those sides are equal, and vice versa
What are the angles of an isocoles right triangle?
What does it look like?
45-45-90
Right triangle means it has a 90 degree angle.
The 2 other angles are equal, so they must be 45 degrees. (angles sum to 180)
What is the area of this triangle?
6
A = 1/2 bh
(1/2 * base * height, where the base and height are perpendicular)
1/2 * 4 * 3 = 6
What is the ratio of the sides of a 45-45-90 right triangle?
If we draw a diagonal across a square, what shapes are formed?
What is the ratio of the sides of a 30-60-90 right triangle?
What is the formula for area of a circle?
πr2
(pi r squared)
What is the area of the circle below with center P?
25π in2
A = πr2
A line that goes across a circle, through the center, is the Diameter
Diameter = 10, so r = 5
What is the formula for circumference of a circle?
2πr or πD (r = radius, D = diameter)
What is the formula for Volume of a Cylinder?
V = πr2h (Area of the circle * height)
If the volume of a cylinder is 45π cubic inches and the height is 5 inches, what is the Diameter of the base?
6 in
V = πr2h
plug in values for V and h: 45π = 5πr2
Divide by 5π on both sideS: 9 = r2
r = 3
Remember to check what’s it’s asking for!
Diameter = 2r = 6 in
What are the 4 quadrants on a graph?
What is the slope of the line that goes through (1,3) and (4,9) ?
What is the equation for slope?
(9-3) / (4-1) = 2
What is the slope of the line below?
2
What does a positive slope look like?
Negative slope?
Zero Slope?
Positive: Goes up as you move from left to right.
Negative: Goes down from left to right
Zero: Horizonal line (parallel to X axis)
What is the Slope-Intercept Equation?
How do we put 4x + 2y = 8 into slope-intercept form?
What is the slope and y-intercept?
Get y by itself:
2y = -4x +8
y = -2x + 4
Slope = -2 , y-intercept = 4
What does the graph of y= -1/2x + 2 look like?
Negative slope of -1/2, y-intercept is 2
Start by drawing the y-intercept, then draw the line using the slope.
For every 1 to the right, we go 1/2 unit down.
What is the “Distance Formula”?
(used to calculate distance between 2 points on a graph)
It is a different form of the Pythagorean Theorem:
What is the distance between the points (0,2) and (-3,-2)?
5
y2-y1 = 2- (-2) = 4
x2 - x1 = 0 - (-3) = 3
32 + 42 = 25
Square root of 25 is 5
We might also notice that the orange triangle is 3-4-5.
This can be a shortcut.
If C is equidistant from points A and B, what does that mean?
It means distance CA = CB
Equidistant means “an equal distance from”.
If A, B, and C were all on the same line, C would be the Midpoint of A and B.
What is the equation for a circle with center at the origin (0,0)?
x2 + y2 = r2
r is the radius and x and y are points on the circle.
