Basic Geometry

Question 1

What is the formula for the area of a rectangle?

Answer 1

Area = length × width

Question 2

True or False: The formula for the circumference of a circle is C = 2πr.

Answer 2

True

Question 3

Fill in the blank: The Pythagorean theorem states that a² + b² = ____.

Answer 3

c²

Question 4

What is the formula for the volume of a cylinder?

Answer 4

Volume = πr²h

Question 5

What is the quadratic formula?

Answer 5

x = (-b ± √(b² - 4ac)) / (2a)

Question 6

What is the formula for the area of a triangle?

Answer 6

Area = 1/2 × base × height

Question 7

True or False: The slope-intercept form of a linear equation is y = mx + b.

Answer 7

True

Question 8

What is the formula for the surface area of a sphere?

Answer 8

Surface Area = 4πr²

Question 9

What is the formula for the sum of the interior angles of a polygon?

Answer 9

Sum = (n - 2) × 180°, where n is the number of sides.

Question 10

Fill in the blank: The formula for the mean of a data set is ____.

Answer 10

Mean = (sum of all values) / (number of values)

Question 11

What is the formula for the area of a trapezoid?

Answer 11

Area = 1/2 × (base1 + base2) × height

Question 12

What is the formula for the distance between two points (x1, y1) and (x2, y2)?

Answer 12

Distance = √((x2 - x1)² + (y2 - y1)²)

Question 13

True or False: The formula for the area of a circle is A = πr.

Answer 13

False

Question 14

What is the formula for the volume of a cone?

Answer 14

Volume = (1/3)πr²h

Question 15

What is the formula for the perimeter of a rectangle?

Answer 15

Perimeter = 2(length + width)

Question 16

Fill in the blank: The formula for compound interest is A = P(1 + r/n)^(nt).

Answer 16

A = Amount, P = Principal, r = rate, n = number of times interest applied per time period, t = time

Question 17

What is the formula for the area of a parallelogram?

Answer 17

Area = base × height

Question 18

What is the formula for the standard deviation of a population?

Answer 18

σ = √(Σ(xi - μ)² / N)

Question 19

True or False: The formula for the volume of a sphere is V = (4/3)πr³.

Answer 19

True

Question 20

What is the formula for the median of a data set?

Answer 20

If n is odd, median = middle value; if n is even, median = average of the two middle values.

Question 21

What is the formula for the slope of a line?

Answer 21

Slope = (y2 - y1) / (x2 - x1)

Question 22

Fill in the blank: The formula for the volume of a rectangular prism is ____.

Answer 22

Volume = length × width × height

Question 23

What is the formula for the area of a sector of a circle?

Answer 23

Area = (θ/360) × πr², where θ is the angle in degrees.

Question 24

What is the formula for the geometric mean of a set of numbers?

Answer 24

Geometric Mean = (n-th root of (x1 × x2 × … × xn))

Question 25

True or False: The formula for the perimeter of a triangle is P = a + b + c.

Answer 25

True

Question 26

What is the formula for the area of a circle?

Answer 26

Area = πr²