Surface Area for a Pyramid

Pyramid is a three dimensional shape. Pyramid has different types . They are rectangular pyramid, square pyramid, hexagonal pyramid and pentagonal pyramid and bases for these pyramids are rectangle, square, hexagon and pentagon respectively. In each type of pyramid , the base will be going to apex narrowly.

The total surface area of a pyramid can be calculated by adding lateral area and base area. If the base is square, we have to find the area of square. The lateral area is perimeter time side length and whole divide by 2.

There are two parts in surface area for a pyramid. They are Lateral area and Base area. The area of base is calculated depends on the shape. For example, for a rectangular pyramid, we use area of rectangle formula. Lateral area is perimeter times side length and whole divided by 2. This looks triangle area formula. So that the sides of pyramids are triangles.

Having problem with Rectangular Prism Surface Area keep reading my upcoming posts, i will try to help you.

The total surface area of a pyramid can be calculated by adding lateral area and base area. If the base is square, we have to find the area of square. The lateral area is perimeter time side length and whole divide by 2.

Surface area for a pyramid formula:

Surface area of a pyramid            = Lateral area + Base area

= 1/2 * perimeter * side length  +  Base area

Let us see the problems on different types of a pyramid for calculating surface area.

Square based pyramid:

sq

Problem 1:

Find the surface area of a square pyramid with the given side 4 cm , height 5 cm, and the slant height 6 cm.

Solution:

Formula:

Surface area of a square pyramid = side2 + 2*side*length

Given :

side = 4 cm, length = slant height = 6 cm

Surface area             = (4)2 + 2 * 4 * 6

=  16 + 48

= 64

Therefore, Surface area of square pyramid is 64 square cm.

Triangular Pyramid:

tri

Problem 2:

Find the surface area of a triangular pyramid with the given apothem length 3 meter, side 4 meter, height 5 meter and the slant height 7 meter.

Solution:

Formula:

Surface area of a triangular pyramid = 1/2 * apothem * side + 3/2 * side * slant height

Given:

Apothem = 3 meter, side = 4 meter, slant height = 7 meter

Surface area of a triangular pyramid              = 1/2 * 3 * 4 + 3/2 * 4 *  7

= 1/2 * 12     + 3/2 * 28

=  12/2         + (3*28)/2

=  6      +    42

= 48

Therefore, the surface area of triangular pyramid is 48 meter2.


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Pentagonal pyramid:

pen

Problem 3:

Find the surface area of pentagonal pyramid with the given apothem length 5 meter, side 6 meter, height 4 meter and the slant height 8 meter.

Solution:

Formula:

Surface area of Pentagonal pyramid = 5/2 * apothem * side + 5/2 * side * slant height

Given :

Apothem = 5 meter, side = 6 meter and slant height = 8 meter.

Surface area of pentagonal pyramid               = 5/2 * 5 * 6 + 5/2 * 6 * 8

= 5/2 * 30     + 5/2  * 48

= (5*30)/2      + (5*48)/2

=  75  + 120

= 195

Therefore, the surface area of pentagonal pyramid is 195 square meters.