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) 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.

Answer 1

Area A B C D = 144 m^2

E F = 6 m

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

Answer 2

144m^2

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