Chapter 11: Extending Volume¶

11.1: Areas of Parallelograms and Triangles¶

Vocabulary

A base of a parallelogram is any side of a parallelogram.
The height of the parallelogram is the length on a line segement perpendicular to the base connect to the opposite side.
The area addition postulate states that the area of a polygon is the sum of all non overlapping parts that make up the polygon.
The base of a triangle can be any side, similar to a parallelogram.
The height of a triangle is the length of an alitude from the base.
The area conguence postulate states that if the triangles are congruent, then the area is congruent.

Triangles and Parallelograms

../_images/111-triangle_in_parallelogram.svg

The height of $A B C E$ from base $\overset{―}{E C}$ is the length of $\overset{―}{A D}$ . According to the area addition postulate, $a r e a o f A B C E = a r e a o f A D E + a r e a o f B A D C$ . The height of $δ A D E$ from base $\overset{―}{A E}$ is the length of $\overset{―}{F D}$ .

11.2: Volumes of Prisms and Cylinders¶

11.3: Volumes of Pyramids and Cones¶

11.4: Spheres¶

11.5: Spherical Geometry¶

11.6: Volume and Nonrigid Transformations¶

11.7: Applying Measurements¶

>Page contents:

Chapter 11: Extending Volume

<Chapter 10: Extending Area

Chapter 12: Probability>

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