Question

Find the total surface area of a pyramid given the base edge is 14 cm and the lateral edge is 9 cm.

• A. $14(7+4\sqrt{2})c{m}^2$
• B. $4\sqrt{2}c{m}^2$
• C. $28(7+4\sqrt{2})c{m}^2$
• D. $84c{m}^2$

Answer 1

The correct option is C

$28(7+4\sqrt{2})c{m}^2$

Given:
Base edge of the pyramid = 14 cm
Lateral edge of the pyramid = 9 cm

$\text{Area of the pyramid}$
$\text{= Area of the base}+4\times (\frac{1}{2}\times base\times slantheight)...\left(i\right)$

Slant height, h $=\sqrt{9^2-7^2}=\sqrt{81-49}=\sqrt{32}=4\sqrt{2}c{m}^2$

Now, from (i)
$\text{Total surface area of the pyramid}$
$=(14\times 14)+4\times (\frac{1}{2}\times 14\times 4\sqrt{2})$

$=196+4\times 7\times 4\sqrt{2}$
$=196+4\times 28\sqrt{2}$
$=28(7+4\sqrt{2})c{m}^2$