Polygon
A two-dimensional, closed shape made of line segments. For example, a triangle is a polygon, as is a rectangle. A circle is a closed shape but it is not a polygon because it does not contain line segments.
Interior Angles
The angles that appear in the interior of a closed shape. The sum of those angles depends only upon the number of sides in the closed shape: (n - 2) * 180 = sum of interior angles, where n = the number of sides in the shape. For example, the interior angles of a four-sided closed shape will always add up to 360° because (4 - 2).
Perimeter
In a polygon, the sum of the lengths of the sides.
Area
The space enclosed by a given closed shape; the formula depends on the specific shape.
Two-
dimensional
A shape containing a length and a width.
Three-dimensional
An object containing a length, a width, and a height.
Triangle
A three-sided closed shape composed of straight lines; the interior angles add up to 180°.
Vertex (singular) or Vertices (plural)
An "angle" or place where two lines of a shape meet; for example, a triangle has three vertices and a rectangle has four vertices.
Legs of a Triangle
The smaller sides of a triangle; usually used in describing a right triangle, in which there is one hypotenuse (the longest side) and two legs (the shorter sides).
Hypotenuse of a Triangle
The longest side of a right triangle. The hypotenuse is opposite the right angle.
Right Triangle
A triangle that includes a 90°, or right, angle.
Area of a Triangle
(base * height) / 2 = area of a triangle, where the base refers to any side of the triangle and the height refers to the length of a line drawn from the opposite vertex to create a 90° angle with that base.
Pythagorean Theorem
A formula used to calculate the sides of a right triangle. a^2 + b^2 = c^2, where a and b are the lengths of the two legs of the triangle and c is the length of the hypotenuse of the triangle.
Parallelogram
A four-sided closed shape composed of straight lines in which the opposite sides are equal and the opposite angles are equal.
Area of a Parallelogram
Area = base * height, where the base refers to any side of the parallelogram and the height refers to the length of a line drawn from one of the opposite vertices to create a 90° angle with that base.
Rectangle
A four-sided closed shape in which all of the angles equal 90° and in which the opposite sides are equal. Rectangles are also parallelograms.
Area of a Rectangle
area = length * width, where length and width refer to the lengths of two adjacent sides of the rectangle.
Rhombus
A four-sided closed shape in which all of the sides are equal and in which the opposite angles are equal. Rhombi are also parallelograms .
Area of a Rhombus
Area = (Diagonal1 * Diagonal2) / 2 , where the diagonals refer to the lengths of the lines drawn between opposite vertices in the rhombus.
Square
A four-sided closed shape in which all of the angles equal 90° and all of the sides are equal. Squares are also rectangles, rhombi, and parallelograms.
Trapezoid
A four-sided closed shape in which one pair of opposite sides is parallel, but the other pair is not parallel.
Area of a Trapezoid
Area = [(Base1 + Base2) * Height ] / 2 , where Base1 and Base2 refer to the two parallel sides, and the height refers to the length of a perpendicular line drawn between the two parallel bases.
Rectangular Solid
A three-dimensional shape consisting of six faces, at least two of which are rectangles (the other four may be rectangles or squares, depending upon the shape’s dimensions).
Surface Area of a Rectangular Solid
Surface area = the sum of the areas of all six faces
Volume of a Rectangular Solid
Volume = length * width * height, where length, width, and height refer to the three dimensions of the rectangular solid.
Cube
A three-dimensional shape consisting of six identical faces, all of which are squares.
Surface Area of a Cube
Surface area = the area of any one face multiplied by 6.
Volume of a Cube
Volume = s^3, where s refers to the length of any one side of the cube.
