Question

SECTION -C
(Questions 27 to 34 carry 3 marks each.)
27. (PISA) :
Below you see a student's mathematical model of a
farmhouse roof with measurements. The attic floor,
ABCD in the model, is a square. The beams that
support the roof are the edges of a 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 of 12 m.
a)
Calculate the area of the attic floor ABCD.
The area of the attic floor ABCD= .
G
b)
12m
Calculate the length of EF, one of the
horizontal edges of the block.
The length of EF =__
m​

Answer 1

Area of the attic floor ABCD. = 144 m² , The length of EF  = 6 m

Step-by-step explanation:

For complete Question see attached picture

area of the attic floor ABCD. = AB * BC

= 12 * 12

= 144 m²

area of the attic floor ABCD. = 144 m²

E is the middle of AT  => ET = AT/2 = 6 m

F is the middle of BT  => FT = BT/2 = 6 m

ΔTEF ≈ ΔTAB

=> ET/AT  = FT/BT  =  EF/AB

=> 6/12 = 6/12 = EF/12

=> EF = 6 m

The length of EF  = 6 m

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