Geometry

Question 1

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

Answer 1

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).

Question 2

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

Answer 2

64

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

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

Question 3

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

Answer 3

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

Question 4

What is true about the sides of a parallelogram?

The angles?

The right triangles created by the yellow lines?

Answer 4

Opposite sides are =

Opposite angles are =

All 4 right triangles are =

Question 5

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

Answer 5

V = LWH (length*width*height)

Question 6

If 2 lines are perpendicular, what does that mean?

Answer 6

They form a right angle.

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

Question 7

What is the pythagorean theorem?

Answer 7

Question 8

Answer 8

3

3² +4² = 5²

The 3-4-5 triangle is good to memorize.

Other right triangles can have the same ratio: 6-8-10, 30-40-50, etc. This is common on the GMAT, and can save time to recognize.

Question 9

What is true about an isocoles triangle?

How do we draw it and identify the properties?

Answer 9

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

Question 10

What are the angles of an isocoles right triangle?

What does it look like?

Answer 10

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)

Question 11

What is the area of this triangle?

Answer 11

6

A = 1/2 bh

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

1/2 * 4 * 3 = 6

Question 12

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

Answer 12

Question 13

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

Answer 13

Question 14

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

Answer 14

Question 15

What is the formula for area of a circle?

Answer 15

πr²

(pi r squared)

Question 16

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

Answer 16

25π in²

A = πr²

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

Diameter = 10, so r = 5

Question 17

What is the formula for circumference of a circle?

Answer 17

2πr or πD (r = radius, D = diameter)

Question 18

What is the formula for Volume of a Cylinder?

Answer 18

V = πr²h (Area of the circle * height)

Question 19

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

Answer 19

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

Question 20

What are the 4 quadrants on a graph?

Answer 20

Question 21

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

What is the equation for slope?

Answer 21

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

Question 22

What is the slope of the line below?

Answer 22

2

Question 23

What does a positive slope look like?

Negative slope?

Zero Slope?

Answer 23

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

Negative: Goes down from left to right

Zero: Horizonal line (parallel to X axis)

Question 24

What is the Slope-Intercept Equation?

Answer 24

Question 25

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

What is the slope and y-intercept?

Answer 25

Get y by itself:

2y = -4x +8

y = -2x + 4

Slope = -2 , y-intercept = 4

Question 26

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

Answer 26

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.

Question 27

What is the “Distance Formula”?

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

Answer 27

It is a different form of the Pythagorean Theorem:

Question 28

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

Answer 28

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.

Question 29

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

Answer 29

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.

Question 30

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

Answer 30

x² + y² = r²

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

The equation comes from the Pythagorean Theorem (a² + b² = c²)

Below is an example, with x=3, y=4, r=5.