a group of 4 students buy movies tickets for $24.At this rate, how much would 20 students pay for the movies

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cmikell124

08.09.2021

Mathematics

Given a cube of sides 4 units with vertices: A, B, C, D, E, F, G, H such that the top square is ABCD and the bottom square is EFGH with AC, BD the diagonals of the top square and EG, FH the diagonals of EFGH.

The shape of the cross-section formed when a plane containing line AC and line EH intersects the cube is the rectangle ACEH.

We obtain the value of line AC which is equal to line EH using the pythagoras rule which states that c^2=a^2+b^2

, where c is the length of line AC, a is the length of line AB = 4 and b is the length of line BC = 4.

Thus,
$c^2=4^2+4^2=16+16=32 \\ c= \sqrt{32} =4 \sqrt{2}$

Therefore, the shape of the cross-section formed when a plane containing line AC and line EH intersects the cube is the rectangle ACEH with length of $4 \sqrt{2}$ units and width of 4 units.

Area of a rectangle is given by
Area = length x width
$=4 \sqrt{2}\times4=16 \sqrt{2}$ square units.

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