Know These Equations- Geometry

Question 1

What is the area of a triangle?

Answer 1

A = 1/2 (base x height)

Question 2

What is the area of a trapezoid?

Answer 2

A = 1/2 [(base1 + base2) x height]

Question 3

What is the area of a parallelogram?

Answer 3

A = base x height

Question 4

What is the area of a rhombus?

Answer 4

A = 1/2 (diagonal1 + diagonal2)

Question 5

What is the volume of a rectangle and/or cube?

Answer 5

Volume = length x width x height

Question 6

What is the area of an Equilateral Triangle?

Answer 6

A = [S²(3^1/2)]/4

–> Where s = side of triangle

Question 7

What equation can be used to find the diagonal of a SQUARE?

Answer 7

d = s(2^1/2)

–> Where s = side of square

Question 8

What equation can be used to find the diagonal of a CUBE?

Answer 8

d = s(3^1/2)

–> Where s = edge (aka side) of cube

Question 9

How do you find the diagonal of a rectangle?

Answer 9

To find the diagonal of a rectangle, one must know EITHER the length and width, OR one dimension and the proportion of one to the other.

With this information, use the Pythagorean Theorem to find the length of the diagonal.

Question 10

What is the Pythagorean Theorem and how is it applied?

Answer 10

a2 + b2 = c2

This theorem states that sum of the square of the two legs of a right triangle is equal to the square of the hypotenuse.

Question 11

How do you find the diagonal of a rectangular solid?

Answer 11

Use the “Deluxe” Pythagorean Theorem d² = x² + y² + z²

–> Where d is the diagonal of the rectangular solid, and x y z are the sides of the rectangular solid

Or, you can use the Pythagorean Theorem twice:

1) First, use said equation to find the diagonal of the bottom face
2) Once the diagonal of the bottom face is found, you can use this as the base leg of another right triangle that is formed by said leg, the true height, and the diagonal of the rectangular solid. Solve for diagonal using Pythagorean Theorem again.

Question 12

What is the area of a circle?

Answer 12

A = πr²

Question 13

What is the circumference of a circle?

Answer 13

C = 2πr

Question 14

What is the surface area of a Cylinder?

Answer 14

SA = 2 circles + rectangle = 2 (πr²) + 2πrh

The only information you need to solve for the surface area of a cylinder is 1) radius of cylinder and 2) height of cylinder

–> This is true bc a cylinder is made up of one rectangle and two circles (at top and bottom). As a result, we know:

• Length of rectangle = circumference of circle
• Width of rectangle = height of cylinder
• Because of the two above, area of rectangle is length x width = (2πr) x height

Question 15

What is the volume of a cylinder?

Answer 15

V = πr²h

Finding the volume of a cylinder depends on 1) radius of cylinder, and 2) height of cylinder

Question 16

How do you calculate the slope of a line?

Answer 16

The slope of a line is calculated by taking the difference of its “rise” (vertical change) and dividing it by the difference in the “run” (horizontal change).

slope = y₂ - y₁ / x₂ - x₁