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

`4.9m`

Explanation:

Determine the center point of the rectangular base:

`1/2` of `3m=1.5m`
`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:

`hypotenuse^2=1.5^2+2.4^2`

hypotenuse`=sqrt(1.5^2+2.4^2)`

hypotenuse`:.=sqrt(8.01`

hypotenuse`:.=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

`:.Slope^2=2.83^2+4^2`

`:.Slope^2=24.0089^2`

`:.slope=sqrt(24.0089)`

`:.4.9m` slope of the pyramid