Area Calculation by Decomposition: Triangles, Rectangles, and Trapezoids

Vocabulary flashcards covering geometric definitions, area formulas, and decomposition techniques for triangles, rectangles, and trapezoids.

Decomposition of a figure

The method of dividing a large figure into smaller figures, calculating the area of each individual part, and summing the results to find the total area.

Right triangle

A triangle that contains an angle of $90^\text{o}$, resembling the corner of a sheet of paper.

Area of a triangle

The measurement obtained by multiplying the base by the height and dividing by $2$, given by $\frac{\text{base} \times \text{height}}{2}$.

Trapezoid

A geometric shape defined by having $2$ parallel bases: one major base and one minor base.

Height of a trapezoid

The perpendicular distance between the $2$ parallel bases of the trapezoid.

Area of a trapezoid

The measurement obtained by adding the major base and the minor base, multiplying the sum by the height, and dividing the result by $2$, given by $\frac{(\text{major base} + \text{minor base}) \times \text{height}}{2}$.

Area of a rectangle

The measurement obtained by multiplying the base by the height, given by $\text{base} \times \text{height}$.

Double-counting constraint in decomposition

The rule stating that when dividing a geometric figure into parts, the exact same region cannot be counted $2$ times.