Question

This square pyramid has a surface area of 16 m2.

Answer 1

Answer:

The surface area increases by 4 times.

Explanation:

Surface area of a square pyramid:

$A =$ $b^{2}$ $+ 2b$ $\sqrt{\frac{b^{2}}{4} +h^{2} }$

Where:

A = surface area

b = base edge

h = height

Doubling the values gives us a b = 4 and h = 6.

Putting those into the equation gives us:

$A = 4^{2} + 2(4) \sqrt{\frac{4^{2}}{4}+6^{2} }$

$A = 16 + 2(4)\sqrt{\frac{4^{2}}{4}+6^{2} }$

$2(4)\sqrt{\frac{4^{2}}{4}+6^{2} } = 16\sqrt{10}$

$A = 16 + 16\sqrt{10}$

And the decimal approximation:

$A = 16 + 16\sqrt{10} = 66.59$

Which roughly equals to 4 times the first surface area.