Question

44 points. find the surface area of the pyramid to the nearest whole number.

Answer 1

It would be 348

as A= lw+l((w /2)^2+h^2)^0.5+w((l /2)^2+h^2)^0.5

where l=12, w=12, h=6

A=347.65 ~ 348

Answer 2

Look at the picture.

Use the Pythagorean theorem:

$h^2=6^2+6^2\\\\h^2=36+36\\\\h^2=72\to h=\sqrt{72}\\\\h\approx8.49\ m$

The surface of the square pyramid is:

one square with a side length of 12m

four triangles with a base length of 12m and a height of 8.49m

The area of a square: $A_\boxed{ }}=12^2=144\ m^2$

The area of a triangle: $A_\Delta=\dfrac{12\cdot8.49}{2}=50.94\ m^2$

The surface area of the pyramid is:

$SA=A_\boxed{ }}+4A_\Delta\\\\SA=144+4\cdot50.94=347.76\approx348 m^2$