Question

The diagram shows a 7cm x 6cm rectangle-based pyramid all the diagonal sides - TA TB TC and TD are length 10cm M is the midpoint of the rectangular base work out the height MT to one decimal place

Answer 1

Given:

The base is a rectangle of dimension 7 cm×6 cm.

The length of each diagonal side = 10 cm

To find the height of MT.

Formula

By Pythagoras theorem we get,

$h^{2} = l^{2} + b^{2}$

where, h be the hypotenuse

b be the base and

l be the height.

Now, in this diagram,

The perpendicular distance of M from BC = 3 cm

Slant height = 10 cm

Taking, b = 3 and h = 10 we get,

$10^{2} = l^{2} + 3^{2}$

or, $l^{2} = 10^2-3^2$

or, $l = \sqrt{100-9}$

or, $l = 9.5$

Hence,

The height of MT is 9.5 cm.