Download Lap 7 Definitions and Conjectures Area: The measure of the region

Lap 7 Definitions and Conjectures
Area: The measure of the region enclosed by the figure. Rectangle Base: Any side of the
rectangle. Rectangle Height: The length of the side perpendicular to the base.
Rectangle/Parallelogram Area Conjecture (C-75)&(C-76): The area of the
rectangle/parallelogram is given by the formula A=bh
Triangle area conjecture (C-77): The area of a triangle is given by the formula A=1/2 bh.
Trapezoid area conjecture (C-78):The area of a trapezoid is given by the formula A=1/2h(b1+b2)
Kite area conjecture (C-79): The area of a kite is given by the formula A=1/2 d1d2
Apothem: Is the perpendicular segment from the center of the polygon’s circumscribed circle
to a side of the polygon.
Regular Polygon Area Conjectures (C-80): The area of a regular polygon is given by the formula
A=1/2nas or A=1/2Pa
Lattice Points: The dots of a square dot grid are called lattice points.
Pick’s Formula: If A is the area of a polygon whose vertices are lattice points, b is the number of
lattice points on the boundary of the polygon, and i is the number of the interior lattice points,
then A=1/2b+i-1
Circle Area conjecture (C-81): The area of a circle is given by the formula A=πr2
Sector of a circle: The region between two radii of a circle and the included arc.
Segment of a circle: The region between a chord of a circle and the included arc.
Annulus: The region between two concentric circles.
Area of the sector: A=a/360πr2. Area of a segment: A=a/360 πr2-1/2bh.
Area of an annulus: A=πR2-πr2
Surface area of a solid: The surface area of a solid is the sum of the areas of all the faces or
surfaces that enclose the solids.
Slant height: The height of each triangular lateral face in a solid.
Hypotenuse: The side opposite the right angle in a right triangle.
Legs: The two sides that create the right angle in a right triangle.
Pythagorean Theorem (C-82): In a right triangle a2+b2=c2
Converse of the Pythagorean Theorem (C-83): If the lengths of the three sides of a triangle
satisfy the Pythagorean equation, than the triangle is right triangle.
Isosceles Right Triangle Conjecture (C-84): In an isosceles right triangle if the lengths have
length l, then the hypotenuse has length l√2.
30-60-90 Triangle conjecture (C-85): In a 30-60-90 Triangle if the shorter leg is a, then the loner
leg is a√3, and the hypotenuse 2a.
Distance formula (C-86): The distance between points A(x1,y1) and B(x2,y2) is given by the
formula AB=√(x2-x1)2+(y2-y1)2
Equation of a circle (C-87): The equation of a circle with radius r and center (h, k) is:
(x-h)2 +(y-k)2=r2