Area Concepts and Formulas

These flashcards cover key vocabulary and formulas related to area from the lecture notes.

Area

The amount of space enclosed within a 2D shape.

Area of a rectangle

Calculated using the formula: Area = base × height (A = bh).

Area of a square

Calculated using the formula: Area = side² (A = s²).

Congruent figures

Figures that have the same shape and size; their areas are equal.

Union of areas

The total area covered by two closed regions, where only the common boundary is counted once.

Area of a parallelogram

Calculated using the formula: Area = base × height (A = bh).

Area of a triangle

Calculated using the formula: Area = 1/2 × base × height (A = 1/2 bh).

Median of a trapezoid

The line segment joining the midpoints of the non-parallel sides of a trapezoid.

Area of a trapezoid

Calculated using the formula: Area = median × height (A = mh).

Apothem

A segment joining the center to the midpoint of a side of a regular polygon.

Area of a regular polygon

Calculated using the formula: Area = 1/2 × apothem × perimeter (A = 1/2 ap).

Hero’s Formula

Used to find the area of a triangle when side lengths are known: A = √[s(s-a)(s-b)(s-c)], where s = semiperimeter.

Brahmagupta’s Formula

Used for cyclic quadrilaterals: A = √[s(s-a)(s-b)(s-c)(s-d)], where s = semiperimeter.

Ratio of areas

The ratio obtained by dividing the area of one figure by the area of another.

Similar triangles

Triangles that have the same shape but not necessarily the same size; their area ratios relate to the squares of the ratio of their corresponding sides.