Question

What is the surface are of a pyramid with a square base length of 3 cm and a slant height of 4 cm?

• A. $15{\text{cm}}^2$
• B. $20{\text{cm}}^2$
• C. $40{\text{cm}}^2$
• D. $33{\text{cm}}^2$

Answer 1

The correct option is D $33{\text{cm}}^2$

We know that a square pyramid has:

• a square base
• 4 side triangular faces

All these triangles are isosceles and congruent, each of which has a side that coincides with a side of the base.

So, the surface area of a square pyramid is the sum of the areas of four of its triangular side faces and the base area.

${\text{Area of the base = (side length)}}^2=3^2=9{\text{cm}}^2$

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

$=\frac{1}{2}\times 3\times 4$

$=\frac{1}{2}\times 3\times 2\times 2$

$=3\times 2$

$=6{\text{cm}}^2$

$\text{Area of four triangular faces}=4\times 6$
$=24{\text{cm}}^2$

$\therefore \text{Total surface area = Area of the base + Area of four triangular faces}$
$=9+24$
$=33{\text{cm}}^2$
Option (d.) is the correct choice.