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

Height MT of the pyramid will be 8.9 cm

    Given in the question,

Since, diagonals of a rectangle bisect each other, point M will be the midpoint of the diagonal AC.

By applying Pythagoras theorem in right triangle ΔABC,

AC² = AB² + BC²

AC =

AC =

AC =

Therefore, AM =

AM = 4.61 cm

Apply Pythagoras theorem in right triangle ΔAMT,

AT² = AM² + TM²

TM =

TM =

     =

     = 8.874

     ≈ 8.9 cm

    Therefore, height MT of the pyramid will be 8.9 cm.

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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,

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,

or,

or,

or,

Hence,

The height of MT is 9.5 cm.