Glossary
Area
The measure of the two-dimensional space enclosed within a flat shape. It quantifies the surface covered by a figure.
Example:
To determine how much paint is needed for a wall, you calculate its area.
Circle
A round plane figure whose boundary consists of points equidistant from a fixed center point. Its area is pi times the radius squared (A = πr²).
Example:
The surface of a pizza is a circle, and its area tells you how much pizza there is to eat!
Composite Shapes
Geometric figures formed by combining two or more basic shapes. Their total area or volume is found by summing the areas or volumes of their individual components.
Example:
An L-shaped swimming pool is a composite shape that can be broken into two rectangles to find its total area.
Cone
A three-dimensional solid with a circular base and a single vertex (apex). Its volume is one-third of the area of its circular base multiplied by its height (V = (πr²h) ÷ 3).
Example:
An ice cream cone holds a specific volume of ice cream, calculated by its formula.
Cube
A special type of rectangular prism where all six faces are identical squares. Its volume is found by cubing the length of one side (V = s³).
Example:
A standard dice is a cube, and its volume is simply the side length cubed.
Cubic Units
The standard units used to measure volume, indicating the number of unit cubes that can fit within a three-dimensional object (e.g., m³, cm³).
Example:
A box that holds 100 small blocks has a volume of 100 cubic units.
Cylinder
A three-dimensional solid with two parallel circular bases connected by a curved surface. Its volume is the area of its circular base multiplied by its height (V = πr²h).
Example:
A soda can is a cylinder, and its volume tells you how much liquid it contains.
Missing Dimensions
Unknown lengths, widths, heights, or radii that must be determined, often by setting up and solving equations, before calculating area or volume.
Example:
To find the volume of a box, you might first need to solve for a missing dimension like its height, given its volume and base area.
Parallelogram
A quadrilateral with two pairs of parallel sides. Its area is found by multiplying its base by its perpendicular height (A = b × h).
Example:
A tilted picture frame might be a parallelogram, and its area is base times height.
Pyramid
A three-dimensional solid with a polygonal base and triangular faces that meet at a single point (apex). Its volume is one-third of the base area multiplied by its height (V = (B × h) ÷ 3).
Example:
The ancient Egyptian structures are famous pyramids, and their volume represents the massive amount of stone used.
Reasonableness (of answer)
The practice of evaluating whether a calculated answer makes logical sense in the context of the problem. It helps catch significant calculation errors.
Example:
If you calculate the area of a small desk to be 500 square meters, checking the reasonableness of your answer would tell you it's likely incorrect.
Rectangle
A quadrilateral with four right angles, where opposite sides are equal in length. Its area is found by multiplying length by width (A = l × w).
Example:
A standard door is a rectangle, and its area helps determine the size of a decorative decal.
Rectangular Prism
A three-dimensional solid with six rectangular faces, also known as a box. Its volume is calculated by multiplying its length, width, and height (V = l × w × h).
Example:
A shoebox is a rectangular prism, and its volume determines how many shoes it can fit.
Sphere
A perfectly round three-dimensional object where every point on its surface is equidistant from its center. Its volume is four-thirds pi times the radius cubed (V = (4/3)πr³).
Example:
A basketball is a sphere, and its volume determines how much air it can hold.
Square
A special type of rectangle where all four sides are equal in length. Its area is calculated by squaring the length of one side (A = s²).
Example:
A chessboard is made of many small square tiles, each with an area of s².
Square Units
The standard units used to measure area, indicating the number of unit squares that can fit within a two-dimensional shape (e.g., cm², ft²).
Example:
If a rug measures 5 feet by 7 feet, its area is 35 square units, or 35 ft².
Trapezoid
A quadrilateral with at least one pair of parallel sides. Its area is calculated by averaging the lengths of the parallel sides and multiplying by the height (A = ((a + b) × h) ÷ 2).
Example:
A common road sign for a yield is shaped like a trapezoid, and its area can be found using the formula.
Triangle
A polygon with three sides and three angles. Its area is half the product of its base and perpendicular height (A = (b × h) ÷ 2).
Example:
The sail of a boat is often a triangle, and its area helps determine the wind force it can capture.
Unit Conversions
The process of changing a measurement from one unit to another (e.g., centimeters to meters) while maintaining its value. This is crucial for consistent calculations.
Example:
Before calculating the volume of a room, you might need to perform unit conversions to ensure all dimensions are in the same unit, like meters.
Volume
The measure of the three-dimensional space occupied by an object. It quantifies how much a container can hold.
Example:
The amount of water a bathtub can hold is its volume.