SURFACE AREA OF PYRAMID WORKSHEET

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Problem 1 : 

Find the surface area of the pyramid shown below.

Problem 2 : 

Find the surface area of the pyramid shown below.

Problem 3 :

Find the surface area of the pyramid shown below.

Solutions

Problem 1 : 

Find the surface area of the pyramid shown below.

Solution : 

Surface area of the pyramid is

=  Sum of areas of all 5 faces

In the above pyramid, the base is a square with side length 5 cm and each wall is a triangle with base 5 cm and height 8 cm.

Let us find the area of each face separately. 

Area of the base  =  5 x 5  =  25 sq.cm

Area of each side wall  =  (1/2) x 5 x 8  =  20 sq.cm 

Area of all 4 side walls  =  4 x 20  =  80 sq.cm 

Surface area of the above pyramid is

=  25 + 80

=  105 sq.cm

Problem 2 : 

Find the surface area of the pyramid shown below.

Solution : 

Surface area of the pyramid is

=  Sum of areas of all 4 faces

In the above pyramid, the base is an equilateral triangle with side length 4 cm and each wall is a triangle with base 4 cm and height 6 cm.

Let us find the area of each face separately. 

Area of the base  =  (√3/4) x 4²  =  4√3 sq.cm

Area of each side wall  =  (1/2) x 4 x 6  =  12 sq.cm 

Area of all 3 side walls  =  3 x 12  =  36 sq.cm 

Surface area of the above pyramid is 

=  4√3 + 36

=  4(√3 + 9)  sq. cm

Problem 3 :

Find the surface area of the pyramid shown below.

Solution : 

Surface area of the pyramid is

=  Sum of areas of all 4 faces

In the above pyramid, the base is an equilateral triangle with side length 6 cm and each wall is a triangle with base 6 cm and height 10 cm.

Let us find the area of each face separately. 

Area of the base  =  (√3/4) x 6²  =  9√3 sq.cm

Area of each side wall  =  (1/2) x 6 x 10  =  30 sq.cm 

Area of all 3 side walls  =  3 x 30  =  90 sq.cm 

Surface area of the above pyramid is

=  (9√3 + 90)

=  9(√3 + 10)  sq.cm

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