When people speak of the "area of a rectangle," what they really mean is the
area of a "rectangular region."
POSTULATE : The area of a square is given by:
AREA is always measure in "square units."
AREAS OF RECTANGLES
POSTULATE : AREA CONGRUENCE POSTULATE: congruent figures have the same areas
POSTULATE : AREA ADDITION POSTULATE: the area of a region is the sum of the areas of its non-overlapping parts.
AREAS OF RECTANGLES
Any side of a rectangle or a parallelogram can be considered its "base:"
A segment perpendicular to the base drawn to the opposite side is the
"altitude" or "height."
THEOREM : THE AREA OF A RECTANGLE:
AREAS OF PARALLELOGRAMS, TRIANGLES, AND RHOMBUSES
THEOREM : AREA OF A PARALLELOGRAM:
THEOREM : AREA OF A TRIANGLE:
THEOREM : AREA OF A RHOMBUS:
AREAS OF TRAPEZOIDS
THEOREM : THE AREA OF A TRAPEZOID:
SIMPLIFYING RADICALS
SIMPLIFYING RADICALS
PYTHAGOREAN THEOREM
In a right triangle, the square of the hypotenuse equals the sum of the squares of the legs.
CONVERSE PYTHAGOREAN THEOREM
If the square of one side of a triangle is equal to the sum of the squares of the other two sides, then the triangle is a right triangle.
CONVERSE PYTHAGOREAN THEOREM
SPECIAL RIGHT TRIANGLES
THEOREM : 45° - 45° - 90° THEOREM (ISOSCELES RIGHT TRIANGLE)
SPECIAL RIGHT TRIANGLES
THEOREM : 30° - 60° - 90° THEOREM
AREAS OF REGULAR POLYGONS
CIRCUMSCRIBED AND INSCRIBED POLYGONS
AREA OF REGULAR POLYGONS
THEOREM : The area of a regular polygon is given by the formula:
CIRCUMFERENCES AND AREAS OF CIRCLES
CIRCUMFERENCES AND AREAS OF CIRCLES
Formulas for the circumference of a circle are:
ARC LENGTH AND AREAS OF SECTORSTo find the length of an arc of a circle:
ARC LENGTHS AND AREAS OF SECTORS
To find the area of a sector of a circle:
THEOREM : THE DISTANCE FORMULA
