# Basic Geometry Formulas

**Basic Geometry Formulas **

A quadrilateral is a four-sided polygon. A paralle logram , a rectangle, a square, a rhombus, and a trapezoid are all quadrilaterals.

A circle is a plane figure in which all points are the same distance from the center of the circle. A diameter of a circle is a line segment across the circle through the center. A radius of a circle is a line segment from the center of the circle to a point on the circle.

The perimeter of a plane geometric figure is a measure of the distance around the figure. The distance around a circle is called the circumference. Area is the amount of surface in a region. Volume is a measure of the amount of space inside a figure in space. The surface area of a solid is the total area on the surface of the solid.

When calculating perimeter of composite figures Be Careful!!!!! In most cases, when calculating the perimeter of a composite figure, you have to deduct one of the sides in your formulas. If you don’t, you’ll end up calculating the same side.

**Essential Rules**

**Triangle**

Sum of the measures of the interior angles = 180°

Sum of an interior and corresponding exterior angle = 180°

Rules to determine congruence: SSS Rule, SAS Rule, ASA Rule

**Perimeter**

Triangle: | P = a + b + c |

Rectangle: | P = 2L + 2W |

Square: | P = 4s |

Circle: | C = πd or C = 2πr |

**Area**

Triangle: | A = 1/2bh |

Rectangle: | A = LW |

Square: | A = s^{2} |

Circle: | A = πr^{2} |

Parallelogram: | A = bh |

Trapezoid | A = 1/2h (b_{1} + b_{2}) |

**Volume**

Rectangular solid: | V = LWH |

Cube : | V = s^{3} |

Sphere: | V = (4/3)πr^{3} |

Right circular cylinder: | V = πr^{2}h |

Right circular cone: | V = (1/3) πr^{2}h |

Regular pyramid: | V = (1/3)s^{2}h |

**Surface Area**

Rectangular solid: | SA = 2LW + 2LH + 2WH |

Cube: | SA = 6s^{2} |

Sphere: | SA = 4 πr^{2} |

Right circular cylinder: | SA = 2 πr^{2} + 2 πrh |

Right circular cone: | SA = πr^{2} + πrl |

Regular pyramid: | SA = s^{2} + 2sl |

Trapezoid | SA = (b_{1} + b_{2})h + pH (H = length of the longest
base) |

**Pythagorean Theorem**

It can be used to find the length of the sides of a
triangle and the distance or height between two points . If a and b are the legs
of a right triangle and c is the length of the hypotenuse, then a^{2} + b^{2} = c^{2}

**Principal Square Root Property
**If r

^{2}= s, then r = , and r is called the square root of s .

**Similar Triangles
**The ratios of corresponding sides are equal. The ratio of corresponding
heights is equal to the ratio of corresponding sides.

< 1 = < 4 and < 3 = < 5 because they are alternate interior angles

**Circle**

The measure of an arc equals the measure of the central angle.

Arc length = __measure of central angle__ circumference

Measure of central angle =

The central angle is < ABC. The arc is AC

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