Introduction to right rectangular pyramid

Introduction to right rectangular pyramid:

                  A pyramid is nothing but a solid with a polygon for a base. All the other faces meet at one point. This point is called the apex (it is also called a vertex). Pyramids do not have a cross-section.  They are named according to the shape of the base. The base of a  right rectangular pyramid is always a rectangle. A rectangular pyramid normally has five faces. Four faces of rectangular pyramid are triangles. The base of its is rectangle. Two faces meet at edge.

         The Right rectangular pyramid has eight edges and  five vertices or corners. A Right rectangular pyramid is not seen often in everyday life – unless you live in Egypt ! This solid does not roll and it does not stack on top of another.

Example to Find the Surface Area of a Right Rectangular Pyramid:

Find the surface area of the right rectangular pyramid shown in figure.

                                             

To find the surface area of each type of pyramid, find the area of the base and the area of all the triangular faces and add all these together. To help you do this, draw a net (diagram of all the faces of a three-dimensional object) of the pyramid. We’ll use
the example of the right rectangular pyramid below to illustrate.

       

Surface area of pyramid:
area of base:

A = L * W

   = (20cm)*(10cm)

   = 200 cm.

There are two triangles with a base length of 20cm and a height of 15.8cm.

             A = bh / 2

                = (20 * 15.8) / 2  

                = 316 / 2

                = 158 cm²

There are two triangles with a base length of 10cm and a height of 18cm.

  A = b*h / 2

                = `(10 * 18) / 2`

                = `180 / 2`

                = 90 cm²

Answer:
Surface area of right rectangular pyramid= area of base + area of two triangles with a base length of 10cm and a height of 18cm +area of two triangles with a base length of 20cm and a height of 15.8cm.

200 cm2 + 2 × 158 cm2 = 316 cm2 + 2 × 90 cm2 = 180 cm2
                   Surface area of right rectangular pyramid   = 696 cm

Example to Find the Volume of a Right Rectangular Pyramid:

Find the volume of right rectangular pyramid shown in figure of length = 12cm, width = 12cm, height = 10 cm. .

                                             

Solution:

given the length = 12cm, width = 12cm, height = 10 cm.

The volume of right rectangular pyramid = `1/3` * base * height

                                                                         = `1/3 ` * (length * width) * height.

                                                                         = `1/3` * (12 * 12) * 10

                                                                         = `1/3` * 144 * 10

                                                                         = `1/3 ` * 1440

volume of right rectangular pyramid is 480 cm³