A square pyramid is a pyramid that has a square base and four lateral faces. A Pyramid is a polyhedron that has a base and 3 or greater triangular faces that meet at a point above the base (the apex).
A square pyramid is a three-dimensional shape that has a total of five faces, hence called a pentahedron.
To find surface area of square pyramid, we have two different ways.
Find the surface area of the square pyramid given below.
Example 1 :
Solution :
Method 1 :
Required surface area = Area of base + 4 Area of triangles
Area of base = 33^{2 }==> 1089 in^{2}
Area of triangle = (1/2) x base x height
Area around the shape = 4 x (1/2) x base x height
= 2 x 33 x 51
= 3366 in^{2}
Surface area = 1089 + 3366
= 4455 in^{2}
Method 2 :
Surface area of square pyramid = A + 2 s l
A= area of base, p = side length and l = slant height
= 33^{2} + 2 x 33 x 51
= 1089 + 3366
= 4455 in^{2}
Example 2 :
Solution :
Required surface area = Area of base + 4 Area of triangles
Area of base = 23^{2 }==> 529 cm^{2}
Area of triangle = (1/2) x base x height
Area around the shape = 4 x (1/2) x base x height
= 2 x 34 x 23
= 1564 cm^{2}
Surface area = 529 + 1564
= 2093 cm^{2}
Example 3 :
Solution :
Required surface area = Area of base + 4 Area of triangles
Area of base = 27^{2 }==> 729 mm^{2}
Area of triangle = (1/2) x base x height
Area around the shape = 4 x (1/2) x base x height
= 2 x 27 x 35
= 1890 mm^{2}
Surface area = 729 + 1890
= 2619 mm^{2}
Example 4 :
A roof is shaped like a square pyramid. One bundle of shingles covers
25 square feet. How many bundles should you buy to cover the roof ?
Solution :
Surface area = 2 x 18 x 15
= 540 square feet
Because one bundle of shingles covers 25 square feet, it will take
540 ÷ 25 = 21.6
bundles to cover the roof.
So, you should buy 22 bundles of shingles
May 21, 24 08:51 PM
May 21, 24 08:51 AM
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