Question

A piece of cheese needs to be covered in a paper of area 120 sq cm as shown in the below figure. Find the possible height of the triangular face of the pyramid.

• A. 3 cm
• B. 6 cm
• C. 5 cm
• D. 7 cm

Answer 1

The correct option is D 7 cm

It is given that, total surface area of the square pyramid = 120 sq cm

This pyramid contains one square base and 4 triangular faces.


Base area = side $\times$ side

Side of the square = 6 cm

Base area = 6 $\times$ 6 = 36 sq cm


Total surface area = Base area + 4 $\times$ area of one triangular face

Area of triangular face = $\frac{1}{2}$$\times$ base $\times$ height

Base of the triangle = 6 cm

Let, the height of the triangle = h

Total surface area = Base area + 4 $\times$ area of one triangular face

120 = 36 + 4 $\times$ $\frac{1}{2}$$\times$ 6 $\times$ h

120 - 36 = 12h

84 = 12h

h = $\frac{84}{12}$

= 7 cm

Hence, the possible height of the pyramid = 7 cm