Questions and Answers
What is the area of a rectangle?
Area of rectangular region
What does postulate 17 state about the area of a square?
Area of a square is the square of the lengths of a side, A=s^2
What does postulate 18 state about area congruence?
If two figures are congruent then they have the same area.
What does postulate 19 cover in terms of area addition?
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What does theorem 11.1 describe regarding the area of a rectangle?
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What does theorem 11.2 state about the area of parallelograms?
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What is the formula for the area of a triangle as per theorem 11.3?
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How is the area of a rhombus calculated according to theorem 11.4?
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What is the altitude of a trapezoid?
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What does theorem 11.5 explain about the area of a trapezoid?
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What is the median of a trapezoid according to theorem 11.6?
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What is the formula for the area of a square?
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What is the formula for the area of a rectangle or parallelogram?
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What is the formula for the area of a triangle?
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How is the area of a rhombus calculated?
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What is the formula for the area of a trapezoid?
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What defines the center of a regular polygon?
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What is the radius of a regular polygon?
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What is the central angle of a regular polygon?
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What is the formula to calculate the measure of the central angle of a regular polygon?
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What is the apothem of a regular polygon?
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What does theorem 11.6 state about the area of regular polygons?
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What is the formula for the area of regular polygons?
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How is the circumference of a circle defined?
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What is the formula for the circumference of a circle?
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What is the area of a circle?
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What is the formula for the area of a circle?
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What is pi?
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What is a sector of a circle?
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What is the length of an arc?
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What is the formula for calculating the length of an arc?
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How is the area of a sector defined?
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What is the formula for the area of a sector?
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Study Notes
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).
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Description
Test your knowledge of area concepts in Geometry with these flashcards focusing on Chapter 11. This quiz covers key postulates related to areas of rectangles and squares, as well as area congruence and addition. Perfect for reinforcing your understanding before the test!