Question

What is the total surface area of the square pyramid whose base edge is 6 cm long and the lateral faces are equilateral triangles?

• A. $36(1+\sqrt{3})c{m}^2$
• B. $9\sqrt{3}c{m}^2$
• C. $36c{m}^2$
• D. $56c{m}^2$

Answer 1

The correct option is A

$36(1+\sqrt{3})c{m}^2$

Given,

Side length of the square = 6 cm

Here, the lateral faces are equilateral triangles.
So, the side length of the triangle = 6 cm ( $\because$ side of the triangle sits on the square edge.)

Total surface area = Area of the base + 4 $\times$ Area of the one triangle

Area of the base = Area of the square = Side $\times$ Side = 6 $\times$ 6 = 36 $c{m}^2$

Area of the equilateral triangle = $\frac{\sqrt{3}}{4}sid{e}^2=\frac{\sqrt{3}}{4}\times 6\times 6=\frac{\sqrt{3}}{4}\times 36=9\sqrt{3}c{m}^2$

Total surface area of Pyramid = $36+4\times 9\sqrt{3}=36+36\sqrt{3}=36(1+\sqrt{3})c{m}^2$