Geometry Chapter 11 Test Flashcards

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?

The area of a region is the sum of the area of its non-overlapping parts. Signup and view all the answers

What does theorem 11.1 describe regarding the area of a rectangle?

Area of rectangle equals the product of base and height. Signup and view all the answers

What does theorem 11.2 state about the area of parallelograms?

Area of a parallelogram equals the product of a base and the height to that base. Signup and view all the answers

What is the formula for the area of a triangle as per theorem 11.3?

Area of triangle equals half the product of base and height. Signup and view all the answers

How is the area of a rhombus calculated according to theorem 11.4?

Area of rhombus equals half the product of its diagonals. Signup and view all the answers

What is the altitude of a trapezoid?

Height of any segment perpendicular to a line containing a base from a point on the opposite base. Signup and view all the answers

What does theorem 11.5 explain about the area of a trapezoid?

Area of a trapezoid equals half the product of the height and the sum of the bases. Signup and view all the answers

What is the median of a trapezoid according to theorem 11.6?

Median (m) of a trapezoid is equal to 1/2(b1+b2). Signup and view all the answers

What is the formula for the area of a square?

A=s^2 Signup and view all the answers

What is the formula for the area of a rectangle or parallelogram?

A=bh Signup and view all the answers

What is the formula for the area of a triangle?

A=1/2bh Signup and view all the answers

How is the area of a rhombus calculated?

A=1/2d1d2 Signup and view all the answers

What is the formula for the area of a trapezoid?

A=1/2h(b1+b2) or A=hm Signup and view all the answers

What defines the center of a regular polygon?

Center of the circumscribed circle. Signup and view all the answers

What is the radius of a regular polygon?

Distance from the center to a vertex. Signup and view all the answers

What is the central angle of a regular polygon?

Angle formed by two radii drawn to consecutive vertices. Signup and view all the answers

What is the formula to calculate the measure of the central angle of a regular polygon?

Central angle=360/n where n is the number of sides. Signup and view all the answers

What is the apothem of a regular polygon?

The perpendicular distance from a center to the side. Signup and view all the answers

What does theorem 11.6 state about the area of regular polygons?

Area of all regular polygons is equal to half the product of the apothem and the perimeter. Signup and view all the answers

What is the formula for the area of regular polygons?

A=1/2ap Signup and view all the answers

How is the circumference of a circle defined?

Pi times the diameter, or pi times twice the radius. Signup and view all the answers

What is the formula for the circumference of a circle?

c=πd or c=2πr Signup and view all the answers

What is the area of a circle?

Pi times the radius squared. Signup and view all the answers

What is the formula for the area of a circle?

A=πr^2 Signup and view all the answers

What is pi?

Ratio of the circumference of a circle to its diameter. Signup and view all the answers

What is a sector of a circle?

Region bounded by two radii and an arc of a circle. Signup and view all the answers

What is the length of an arc?

Part of the circumference of the circle. Signup and view all the answers

What is the formula for calculating the length of an arc?

Arc length=angle/360(2πr) Signup and view all the answers

How is the area of a sector defined?

Fraction times the area of a circle. Signup and view all the answers

What is the formula for the area of a sector?

Area of sector=angle/360(πr^2) Signup and view all the answers

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!