Question

The diagram shows a pyramid with a horizontal rectangular base:
The rectangular base has length $4.8m$ and width $3m$ and the height of the pyramid is $4m$.
Calculate:
$y$. the length of a sloping edge of the pyramid.

Answer 1

Center point of the rectangular base

$\frac{1}{2}\times 3=1.5m$

$\frac{1}{2}\times 4.8=2.4m$

The crossing point of two lines $=$ Center 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, with Pythagoras theorem

$(Hypotenuse{)}^2={1.5}^2+{2.4}^2$

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

$=\sqrt{8.01}$

$=2.83m$

It is also adjacent side of vertical right angle triangle with opposite side 4m.

So

In vertical right angled triangle

Hypotenuse $=$ Alope of pyramid

therefore,

$(Slope{)}^2={2.83}^2+4^2$

$=\sqrt{{2.83}^2+4^2}$

$=\sqrt{24.0089}$

$=4.9m$

Hence Slope of the pyramid is 4.9 m.