Geometry Chapter 11 Test Flashcards

Area Formulas

• Area of a rectangle is calculated as A = bh, where b is base and h is height, measured in square units.
• Area of a square is defined as A = s², where s is the length of a side.
• Area of a parallelogram also follows A = bh, with base and height measured at right angles.
• Area of a triangle is represented as A = 1/2bh, noting that base and height meet at a right angle.
• Area of a rhombus is determined using A = 1/2d₁d₂, where d₁ and d₂ are the lengths of the diagonals.
• Area of a trapezoid can be found using A = 1/2h(b₁ + b₂) or A = hm, where m is the median.

Postulates

• Postulate 17 states that the area of a square is the square of the length of its side (A = s²).
• Postulate 18 asserts that congruent figures have the same area, although the converse is not true.
• Postulate 19 indicates that the area of a region is the sum of the areas of its non-overlapping parts.

Geometric Terms

• The altitude of a trapezoid is the height of a segment that is perpendicular to a base from the opposite base.
• The center of a regular polygon is the point at the center of its circumscribed circle.
• The radius of a regular polygon is the distance from the center to one of its vertices.
• The central angle of a regular polygon is formed by two radii extending to consecutive vertices, calculated as central angle = 360/n.

Area and Perimeter of Regular Polygons

• The apothem of a regular polygon is the perpendicular distance from the center to a side, effectively bisecting the central side.
• The area of regular polygons can be calculated using A = 1/2ap, where a is the apothem and p is the perimeter.

Circle Geometry

• The circumference of a circle is determined by c = πd or c = 2πr, linking diameter and radius to the circle’s perimeter.
• Area of a circle is given by A = πr², linking the area to the radius squared.
• Pi (π) is the constant ratio of circumference to diameter, approximated as 22/7 or 3.14.

Sector and Arc Length

• A sector of a circle is the area bounded by two radii and an arc.
• Length of an arc is a portion of the circle's circumference, calculated as arc length = (angle/360) × (2πr).
• Area of a sector is a fraction of the circle's total area, given by area of sector = (angle/360) × (πr²).