Question

the base of a right pyramid with a square is a square ABCD of side 10 cm the length of its slant Edge is 15 cm calculate the height of the pyramid the surface area of the pyramid the area of the pyramid​

Answer 1

Solution

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Correct option is A)

We first calculate slant height L of the pyramid with base s=10 cm and height 12 cm:

L 2 =H 2 +( 2s )

2

=12

2

+(

2

10

)

2

=12

2

+5

2

=144+25=169

⇒L=

169

=13

The perimeter of the base is P=4s, since it is a square, therefore,

P=4×10=40 cm

The general formula for the lateral surface area of a regular pyramid is LSA=

2

1

Pl where P represents the perimeter of the base and l is the slant height.

Since the perimeter of the pyramid is P=40 cm and the slant height is l=13 cm, therefore, the lateral surface area is:

LSA=

2

1

Pl=

2

1

×40×13=260 cm

2

Now, the area of the base B=s

2

with s=10 cm is:

B=s

2

=10

2

=100 cm

2

The general formula for the total surface area of a regular pyramid is TSA=

2

1

Pl+B where P represents the perimeter of the base, l is the slant height and B is the area of the base.

Since LSA=

2

1

Pl=260 cm

2

and area of the base is B=100 cm

2

, therefore, the total surface area is:

TSA=

2

1

Pl+B=260+100=360 cm

2

Hence, total surface area of the pyramid is 360 cm

2

.