The diagram shows a 7cm x 6cm rectangle-based pyramid

all the diagonal sides - TA, TB, TC, TD are the length 10 cm

M is the midpoint of the rectangular based.

work out the hight MT. give your answer to 1 decimal place
show your working out

MT = 8.9 cm

Step-by-step explanation:

In the rectangle ABCD, Angle ABC = 90 degree

In the triangle ABC, Angle B = 90 degree

=> ABC is the right angle triangle

According to the Pythagoras theorem, we have the following equation:

+)

⇔

⇔

⇔ cm

In the rectangle ABCD, M is the midpoint, so that it is also the midpoint of line segment AC.

=> AM = cm

TM is the height of the pyramid, so that it is perpendicular to the base ABCD.

As AM belongs to the surface of the rectangle ABCD

=> TM is also perpendicular to AM

=> AMT is the right-angled triangle with Angle AMT = 90 degree

According the Pythagoras theorem, we have the following equation:

⇔

⇔

⇔ ≈ 8.9 cm

MT = 8.9 cm

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step-by-step explanation:

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