Math Review: Pythagoras, Quadrilaterals, 3D Shapes, and Trigonometry

Vocabulary flashcards covering geometry and trigonometry concepts including Pythagoras, Quadrilaterals, 3D Shapes, and SOH CAH TOA.

Pythagorean Theorem

A mathematical formula $a^2 + b^2 = c^2$ used to determine the hypotenuse $c$ or unknown side lengths $a$ and $b$ of a right-angled triangle.

Rhombus

A quadrilateral that has $4$ equal sides and opposite sides parallel, but contains no right angles.

Square (as a Rectangle)

A shape that is also classified as a rectangle because it fulfills the definition of having four right angles and opposite equal sides.

Volume of a Rectangular Box

The amount of 3D space enclosed by a rectangular prism, calculated using $V = l \times b \times h$; for $l = 10\,\text{cm}$, $b = 4\,\text{cm}$, and $h = 5\,\text{cm}$, the volume is $200\,\text{cm}^3$.

Surface Area of a Rectangular Box

The total outer area of a rectangular prism, calculated using $\text{Surface Area} = 2(lb + bh + lh)$; for $l = 10\,\text{cm}$, $b = 4\,\text{cm}$, and $h = 5\,\text{cm}$, the area is $184\,\text{cm}^2$.

Volume of a Cylinder

The 3D space within a cylinder given by $V = \pi r^2 h$; using radius $r = 7\,\text{cm}$, height $h = 10\,\text{cm}$, and $\pi = \frac{22}{7}$, the volume is $1540\,\text{cm}^3$.

Cube Volume and Surface Area

For a cube with side length $s = 3\,\text{cm}$, its volume is $V = s^3 = 27\,\text{cm}^3$ and its surface area is $\text{Surface Area} = 6s^2 = 54\,\text{cm}^2$.

SOH CAH TOA

A mnemonic defining right-triangle trigonometric ratios: $\sin(\theta) = \frac{\text{opposite}}{\text{hypotenuse}}$, $\cos(\theta) = \frac{\text{adjacent}}{\text{hypotenuse}}$, and $\tan(\theta) = \frac{\text{opposite}}{\text{adjacent}}$.

Sine Ratio

The trigonometric ratio $\sin(\theta) = \frac{\text{opposite}}{\text{hypotenuse}}$; for a triangle with opposite side $6$ and hypotenuse $10$, $\sin(\theta) = 0.6$.

Cosine Ratio

The trigonometric ratio $\cos(\theta) = \frac{\text{adjacent}}{\text{hypotenuse}}$; for adjacent side $5\,\text{cm}$ and hypotenuse $10\,\text{cm}$, $\cos(\theta) = 0.5$.