# 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 .

Apr 11, 2017

$4.9 m$

#### Explanation:

Determine the center point of the rectangular base:

$\frac{1}{2}$ of $3 m = 1.5 m$
$\frac{1}{2}$ of $4.8 m = 2.4 m$

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:

$h y p o t e \nu s {e}^{2} = {1.5}^{2} + {2.4}^{2}$

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

hypotenuse:.=sqrt(8.01

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

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

$\therefore S l o p {e}^{2} = {2.83}^{2} + {4}^{2}$

$\therefore S l o p {e}^{2} = {24.0089}^{2}$

$\therefore s l o p e = \sqrt{24.0089}$

$\therefore 4.9 m$ slope of the pyramid