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Area Formulas

Rectangle - L x W

Parallelogram - B x H

Square - (side)squared

Trapezoid - (base1 + base 2)/2 x height

Trapezoid

A quadrilateral with one pair of parallel sides and one pair of nonparallel sides.

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Square

A rectangle with four equal sides.

Area = Side²

Perimeter = 4s

Parallelogram

A parallelogram has two pairs of parallel sides.

- Opposite sides are equal
- Consecutive sides add up to 180 degrees

Rectangle

A four-sided figure with four angles.

- Opposite sides are equal
- Diagonals are equal

Special Right Triangles

(45-45-90)

The sides of a 45-45-90 triangle have a ratio of 1:1:√2

Special Right Triangles

(30-60-90)

The sides of a 30-60-90 triangle have a ratio of:

1:√3:2

Special Right Triangles

(5-12-13)

A triangle is a 5-12-13 when it has a leg to leg ratio of 5:12 or a leg to hypotenuse ratio of 5:13 or 12:13.

Solve for what multiplicity of 5-12-13 it is.

Special Right Triangles

(3-4-5)

A triangle is a 3-4-5 when it has a leg to leg ratio of 3:4 or a leg to hypotenuse ratio of 3:5 or 4:5.

Solve by finding what multiplicity of 3-4-5 it is.

Pythagorean Theorm

a² + b² = c²

Area of a Triangle

1/2 base x height

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Similar Triangles

Similar triangles have the same shape. Corresponding angles are equal and corresponding sides are proportional.

Exterior angles of a triangle

To solve for an exterior angle, find the sum of the remote interior angles.

Exterior angles add up to 360 degrees

Interior angles of a triangle

The three angles of any triangle add up to 180 degrees

Intersecting lines

When two lines intersect, adjacent angles are supplementary (equal to 180 degrees) and vertical angles are equal.

Parallel Lines and Transversals

A transversal across parallel lines forms four equal acute angles and four equal obtuse angles.

Area of a Sector

When n = the sector's central angle

A = (n/360)(Πr²)

Surface area of a rectangular solid

2lw + 2wh + 2lh

Volume of a rectangular solid

V = lwh

Volume of a cube

When e = the length of the edge of a cube

V = e³

volume of a cylinder

V = Πr²h

Volume of a cone

V = 1/3Πr²h

Volume of a sphere

V = 4/3Πr³

Length of an arc

When n = the arc's central angle (n/360)(2Πr)

Circumference of a circle

2Πr

Interior angles of a polygon

Sum of the angles = (n-2) x 180 To find one angle = (n-2) x 180 --------------------------- n

Sohcahtoa & cotangent, secant, and cosecant

Sine - opposite/hypotenuse Cosine - adjacent/hypotenuse Tangent - opposite/adjacent Cotangent - adjacent/opposite Secant - hypotenuse/adjacent Cosecant - hypotenuse/opposite

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