Question

How to find a sloping edge of a rectangular based pyramid? The rectangular based has length 4.8m and width 3m and the height of the pyramid is 4m .

Answer 1

Determine the center point of the rectangular base:
$\frac{1}{2}$ of $3m=1.5m$
$\frac{1}{2}$ of $4.8m=2.4m$

The crossing point of the two lines= centre point of the rectangle.

This centre point is also the bottom of the perpendicular height of 4m given.

Draw a line from the corner of the rectangle to the centre of the rectangle.

So: In the horizontal right triangle= adjacent side=1.5m and opposite.side=2.4m

With Pythagoras:

$hypotenus{e}^2={1.5}^2+{2.4}^2$

hypotenuse = $\sqrt{{1.5}^2+{2.4}^2}$

Hypotenuse $\therefore =\sqrt{8.01}$

hypotenuse $\therefore =2.83m$also adjacent side of vertical right angle triangle with Opposite side given=4m

So: In the vertical right triangle the hypotenuse = slope of pyramid

$\therefore Slop{e}^2={2.83}^2+4^2$

$\therefore Slop{e}^2={24.0089}^2$

$\therefore slope=\sqrt{24.0089}$

$\therefore 4.9m$ slope of the pyramid.