Answer:
144m^2
Step-by-step explanation:
The attic floor, ABCD in the model, is a square. The beams that support the roof are the edges of a block (rectangular prism) EFGHIJKLMN. 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. a Calculate the area of the attic floor ABCD.
the shape is a pyramid. of course we know the pyramid has the edge to be of length 12m.
we know also that the area of the square base of the pyramid will be
Area=length*length
Area of ABCD=L^2
12*12
=144m^2
Answer:
Area A B C D = 144 m^2
E F = 6 m
Step-by-step explanation:
Given:
All Edges of the pyramid L = 12 m
And points E , F , G , H are mid-points of Lengths A T , B T , C T ,D T.
Floor is a square with a = Edges of the pyramid L = 12 m.
a. The area of the attic floor A B C D:
Since the area is a square A = a^2 = L^2 = 12^2 = 144 m^2
Answer: Area (A B C D) = 144 m^2
b. Length E F or one of the horizontal edges of the block:
We will scrutinize on the plane <A T B> on the pyramid.
Apply property of similar triangles on <A T B> & <E T F>:
Where, Angle T is common between both triangles, angle <T A B> and angle < T E F >, angle < T B A > and angle < T F E > are corresponding angles; hence ,
E F / AB = T F / TB
E F = ( T F / TB ) * AB = ( 0.5*TB / TB ) * (12) = 6 m
Answer: E F = 6 m
