Question

The height of a tent in the shape of hexagonal pyramid is increased as shown in the below figure. Find the change in surface area.

• A. 1,600 sq in
• B. 2000 sq in
• C. 1,800 sq in
• D. 1,200 sq in

Answer 1

The correct option is D 1,200 sq in

The given hexagonal pyramid contains one base and 6 lateral faces in triangular form.

Figure 1:

Surface area = Base area + area of 6 triangular faces

Base area = 3600 sq in

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

Base of the triangle = 40 in

Height of the triangle = 84 in

Area of the triangular face = $\frac{1}{2}$$\times$ 40 $\times$ 84

= 1680 sq in

Total surface area = 3600 + 6 $\times$ 1680

= 3600 + 10080 = 13,680 sq in



Figure 2:

Height of the triangle = 94 in

Base of the triangle = 40 in

Area of the triangular face = $\frac{1}{2}$$\times$ 40 $\times$ 94

=1880 sq in

Total surface area = 3600 + 6(1880) = 3600 + 11280

= 14880 sq in



Difference in surface area = 14880 - 13680

= 1200 sq in

Hence, the difference in surface area = 1,200 sq in