Question

The attic floor, ABCD in the model, is a square. The beams that support the roof are the edges of a block (rectangular prism) EFGHKLMN. E is the middle of AT, F is the middle of BT, G is the middle of CT and H is the middle of DT. All the edges of the pyramid in the model have length 12m.
Calculate the length of EF, one of the horizontal edges of the block.

Answer 1

Answer:

EF = 6m.

Step-by-step explanation:

Given that:

1) All the edges of the pyramid in the model have length 12m.

So, AB = 12m

2) E is the middle of AT, F is the middle of BT

So, EF is a line segment connecting the midpoints of ΔATB

So, by applying The Triangle Mid-segment Theorem

EF // AB and EF = 0.5 AB

So, EF = 0.5 AB = 0.5 * 12 = 6m

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The Triangle Mid-segment Theorem:

The line segment connecting the midpoints of any two sides of a triangle has the following properties:

1) The line segment will be parallel to the third side.

2) The length of the line segment will be a half of the length of the third side.