Q10: Geometry Flashcards

1
Q

What is the area of a rectangular field that is 25 feet long, 12 feet wide?

A

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).

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2
Q

What is the perimeter of a rectangle with length 19 and width 13?

A

64

P = 2(L+W) = 2*32 =64

or, 2L+2W, but this is 3 steps to calculate instead of 2

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3
Q

If a rectangle has an area of 100, what is the minimum perimeter?

A

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

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4
Q

What is the formula for volume of a rectangular solid? (also known as a “rectangular prism”)

A

V = LWH (length*width*height)

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5
Q

If 2 lines are perpendicular, what does that mean?

A

They form a right angle.

It is indicated by the square symbol below (dotted gray line)

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6
Q

What is the pythagorean theorem?

A
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7
Q

What is the formula for the diagonal of a rectangular solid?

A

This is called the Deluxe Pythagorean Theorem

(Pythagorean Theorem applied to 3 dimensions)

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8
Q
A

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.

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9
Q

What is true about an isocoles triangle?

How do we draw it and identify the properties?

A

If 2 sides are equal, the 2 angles opposite those sides are equal, and vice versa

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10
Q

What are the angles of an isocoles right triangle?

What does it look like?

A

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)

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11
Q

What is the area of this triangle?

A

6

A = 1/2 bh

(1/2 * base * height, where the base and height are perpendicular)

1/2 * 4 * 3 = 6

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12
Q

What is the ratio of the sides of a 45-45-90 right triangle?

A
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13
Q

If we draw a diagonal across a square, what shapes are formed?

A
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14
Q

What is the ratio of the sides of a 30-60-90 right triangle?

A
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15
Q

What is the formula for area of a circle?

A

πr2

(pi r squared)

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16
Q

What is the area of the circle below with center P?

A

25π in2

A = πr2

A line that goes across a circle, through the center, is the Diameter

Diameter = 10, so r = 5

17
Q

What is the formula for circumference of a circle?

A

2πr or πD (r = radius, D = diameter)

18
Q

What is the formula for Volume of a Cylinder?

A

V = πr2h (Area of the circle * height)

19
Q

If the volume of a cylinder is 45π cubic inches and the height is 5 inches, what is the Diameter of the base?

A

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

20
Q

What are the 4 quadrants on a graph?

A
21
Q

What is the slope of the line that goes through (1,3) and (4,9) ?

What is the equation for slope?

A

(9-3) / (4-1) = 2

22
Q

What is the slope of the line below?

A

2

23
Q

What does a positive slope look like?

Negative slope?

Zero Slope?

A

Positive: Goes up as you move from left to right.

Negative: Goes down from left to right

Zero: Horizonal line (parallel to X axis)

24
Q

What is the Slope-Intercept Equation?

A
25
Q

How do we put 4x + 2y = 8 into slope-intercept form?

What is the slope and y-intercept?

A

Get y by itself:

2y = -4x +8

y = -2x + 4

Slope = -2 , y-intercept = 4

26
Q

What does the graph of y= -1/2x + 2 look like?

A

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.

27
Q

What is the “Distance Formula”?

(used to calculate distance between 2 points on a graph)

A

It is a different form of the Pythagorean Theorem:

28
Q

What is the distance between the points (0,2) and (-3,-2)?

A

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.

29
Q

If C is equidistant from points A and B, what does that mean?

A

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.

30
Q

What is the equation for a circle with center at the origin (0,0)?

A

x2 + y2 = r2

r is the radius and x and y are points on the circle.