Understanding Part Shapes

Overview

We studied about 2D shapes

• squares,

• rectangles,

• triangles,

• polygons, and

• circles
These are some of the standard shapes.

Some part-shapes can be derived from these standard shapes. One of the method is to cut the shapes with straight lines and part of the standard shape is analyzed for perimeter or area.

The following are studied
• the perimeter and area of sectors and segments.
• the surface area and volume of frustum.

slicing rectangle

Consider slicing rectangle as shown in the figure. The possible shapes formed in slicing a rectangle with a straight line are

triangle

rectangle

or
quadrilateral.

Part shapes are illustrated in the figure.

It is noted that for polygons, the part-shape will be another polygon.

slicing circle

When a circle is sliced with a line, the shapes formed are "sector and segment", as shown in the figure.

Sector and Segment are studied in Geometry. In mensuration, the interest is in finding the perimeter and area of the part-shapes. In particular, the perimeter and area of sectors and segments are studied.

solids

We studied about 3D solids

• cubes,

• cuboids,

• cylinders,

• cones,

• prisms,

• pyramids, and

• spheres
These are some of the standard solids.

Some part-solids can be derived from these standard shapes. One of the method is to cut the shapes with a plane and part of the standard shape is analyzed for surface area or volume.

Consider slicing a cuboid and a cylinder with a plane as shown in the figure. For this course, we restrict ourselves to planes parallel to one of the faces. The part-solids are formed from this are a cuboid and a cylinder.

slicing cone

When a cone is sliced with a plane, the part-solid formed are shown in the figure. The two part-solids of cone are a cone and a frustum

summary

The part-shaped formed by planes, that are not parallel to a face of the solid, are outside the scope of this course. In mensuration, the interest is in finding the surface area and volume of the part-shapes. In particular, the following are studied

• the perimeter and area of sectors and segments.
• the surface area and volume of frustum.

Outline

The outline of material to learn *Mensuration : Length, Area, and Volume* is as follows.

Note 1: * click here for the detailed overview of Mensuration High *

Note 2: * click here for basics of mensuration, which is essential to understand this. *

• ** Basics of measurement**

→ __Summary of Measurement Basics__

→ __Measurement by superimposition__

→ __Measurement by calculation__

→ __Measurement by equivalence__

→ __Measurement by infinitesimal pieces__

→ __Cavalieri's Principle (2D)__

→ __Cavalieri's Principle (3D)__

• **Perimeter & Area of 2D shapes**

→ __Circumference of Circles__

→ __Area of Circles__

• **Surface area & Volume of 3D shapes**

→ __Prisms : Surface Area & Volume__

→ __Pyramids : Surface Area & Volume__

→ __Cone : Surface Area & Volume__

→ __Sphere : Surface Area & Volume__

• **Part Shapes **

→ __Understanding part Shapes__

→ __Circle : Sector and Segment__

→ __Frustum of a Cone__