Geometry Chapter 11 Review Flashcards

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Questions and Answers

What is the area of a square?

The squared length of a side

If two figures are congruent, what can be said about their area?

They have the same area

What is the area of a region?

The sum of the areas of its non-overlapping parts

How do you calculate the area of a rectangle?

The product of its base and height Signup and view all the answers

What is the area of a parallelogram?

A base and the height to that base Signup and view all the answers

The area of a triangle equals...

Half the product of a base and the height to that base Signup and view all the answers

How is the area of a rhombus calculated?

Half the product of its diagonals Signup and view all the answers

What is the area of a trapezoid?

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?

Half the sum of the bases Signup and view all the answers

What is the Center of a Regular Polygon?

The center of the circumscribed circle Signup and view all the answers

What defines the Radius of a Regular Polygon?

The distance from the center to a vertex Signup and view all the answers

What is a Central Angle of a Regular Polygon?

An angle formed by two radii drawn to consecutive vertices Signup and view all the answers

Define the Apothem of a Regular Polygon.

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

How is the area of a regular polygon determined?

Half the product of the apothem and the perimeter Signup and view all the answers

What is the formula for the circumference of a circle?

2πr Signup and view all the answers

What is the area formula of a circle?

πr^2 Signup and view all the answers

What is a Sector of a circle?

A region bounded by two radii and an arc of the circle Signup and view all the answers

If two triangles have equal heights, how does the ratio of their areas relate?

The ratio of their bases Signup and view all the answers

If two triangles have equal bases, how does the ratio of their areas relate?

The ratio of their heights Signup and view all the answers

If two triangles are similar, how does the ratio of their areas relate?

The square of their scale factor Signup and view all the answers

If the scale factor of two similar figures is a:b, what can be said about the ratio of their perimeters?

a:b Signup and view all the answers

If the scale factor of two similar figures is a:b, how is the ratio of their areas expressed?

a^2:b^2 Signup and view all the answers

What is the probability that point P is on segment AC if point P of segment AB is picked at random?

length of AC/length of AB Signup and view all the answers

What is the probability that point P is in region R if point P of region S is picked at random?

area of R/area of S Signup and view all the answers

Study Notes

Area of Shapes

The area of a square is calculated by squaring the length of one side.
Congruent figures have identical areas.
The area of a region is found by summing the areas of its non-overlapping parts.
For rectangles, area is the product of its base and height.
The area of a parallelogram is derived from multiplying a base by the height associated with it.
The area of a triangle is half the product of its base and height.
A rhombus' area is calculated as half the product of its diagonals.
The area of a trapezoid is determined by half the product of its height and the sum of its bases.

Properties of Trapezoids

The median of a trapezoid represents half of the sum of its bases.

Regular Polygons

The center of a regular polygon is the point at the center of its circumscribed circle.
The radius of a regular polygon measures the distance from its center to any of its vertices.
A central angle in a regular polygon is formed by two radii connecting consecutive vertices.
The apothem is the perpendicular distance from the center of the polygon to one of its sides.
The area of a regular polygon can be calculated as half the product of its apothem and its perimeter.

Circle Properties

The circumference of a circle can be calculated using the formula 2πr.
The area of a circle is given by the formula πr².
A sector of a circle consists of a region defined by two radii and the arc between them.

Triangle Area Ratios

For triangles with equal heights, the area ratios correspond to the ratios of their bases.
For triangles with equal bases, the area ratios match the ratios of their heights.
Similar triangles have area ratios that equal the square of their scale factor.

Ratios and Scale Factors

For two similar figures with a scale factor a:b, their perimeter ratios will be a:b.
The area ratio of similar figures with a scale factor a:b will be a²:b².

The probability of a randomly chosen point P on segment AB being on segment AC is the ratio of the length of AC to the length of AB.
When selecting a point P randomly within a larger region S, the probability of it being in a smaller region R is the ratio of the area of R to the area of S.

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Description

Test your understanding of geometry concepts with this review of Chapter 11. These flashcards cover essential terms and definitions related to areas of various shapes. Perfect for quick revision and enhancing your geometry knowledge.