Surface area of a Pyramid is an important concept of study under Geometry. Geometry deals with the study of 2 dimensional shapes and 3 dimensional solids. Pyramids are solids with a base and one vertex. Students can learn about working problems associated to solids and they can get help with Geometry problems from the online tutors.
Introduction about find surface area of a pyramid:
Pyramid is a three dimensional object. There are different types of pyramid. They are square pyramid, rectangular pyramid, hexagonal pyramid and pentagonal pyramid and bases for these pyramids are square, rectangle, hexagon and pentagon respectively. The total surface area of a pyramid can be calculated by adding lateral area and base area. If the base is rectangle, we have to find the area of rectangle. The lateral area is perimeter time side length and whole divide by 2.
Introduction about find surface area of a pyramid:
Pyramid is a three dimensional object. There are different types of pyramid. They are square pyramid, rectangular pyramid, hexagonal pyramid and pentagonal pyramid and bases for these pyramids are square, rectangle, hexagon and pentagon respectively. The total surface area of a pyramid can be calculated by adding lateral area and base area. If the base is rectangle, we have to find the area of rectangle. The lateral area is perimeter time side length and whole divide by 2.
Pentagonal pyramid:
Formula:
Surface area of Pentagonal pyramid =5/2 x apothem x side + 5/2 x side x slant height
Problem 2:
Example: Find the surface area of pentagonal pyramid with the given apothem length 7 meter, side 5 meter, height 6 meter and the slant height 9 meter.
Solution:
Given:
Apothem = 7 meter, side = 5 meter and slant height = 9 meter.
Surface area of pentagonal pyramid = 5/2x 7 x 5 + 5/2 x 5 x 9
= 5/2 x 35 + 5/2 x 45
= 87.5 + 112.5
= 200
The surface area of pentagonal pyramid is 200 square meters.
Example: Find the surface area of pentagonal pyramid with the given apothem length 7 meter, side 5 meter, height 6 meter and the slant height 9 meter.
Solution:
Given:
Apothem = 7 meter, side = 5 meter and slant height = 9 meter.
Surface area of pentagonal pyramid = 5/2x 7 x 5 + 5/2 x 5 x 9
= 5/2 x 35 + 5/2 x 45
= 87.5 + 112.5
= 200
The surface area of pentagonal pyramid is 200 square meters.
Formula:
Surface area of a triangular pyramid = 1/2 x apothem x side + 3/2 x side x slant height
Example : Find the Surface area of a triangular pyramid with the given apothem length 4 meter, side 5 meter, height 6 meter and the slant height 8 meter.
Solution:
Given:
Apothem = 4 meter, side = 5 meter, slant height = 8 meter
Surface area of a triangular pyramid = 1/2 x 4 x 5 + 3/2 x 5 x 8
=1/2 x 20 + 3/2 x 40
= 10 + 60
= 70
The surface area of triangular pyramid is 70 meter2.
Area of a Pyramid with a Square Base
Square based pyramid:Formula:
Surface area of a square pyramid = side2 + 2 x side x length
Solution:
Given:
side = 5 cm, length = slant height = 9cm
Surface area = (5)2 + 2 x 5 x 9
= 25 + 90
= 115
The Surface area of pyramid is 115 square cm
Students can get help with Geometry homework associated with Pyramids and problems from the online tutors.
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