SURFACE AREA IF SQUARE BASE PYRAMID

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 sum of areas of all sides
• Using formula

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 = 33² ==> 1089 in²

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 in²

Surface area = 1089 + 3366

= 4455 in²

Method 2 :

Surface area of square pyramid = A + 2 s l

A= area of base, p = side length and l = slant height

= 33² + 2 x 33 x 51

= 1089 + 3366

= 4455 in²

Example 2 :

Solution :

Required surface area = Area of base + 4 Area of triangles

Area of base = 23² ==> 529 cm²

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 cm²

Surface area = 529 + 1564

= 2093 cm²

Example 3 :

Solution :

Required surface area = Area of base + 4 Area of triangles

Area of base = 27² ==> 729 mm²

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 mm²

Surface area = 729 + 1890

= 2619 mm²

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