Question

What is the shape of the cross-section formed when a plane containing line ac and line eh intersects this cube? what is the area of the cross-section? in two or more complete sentences, explain how you were able to determine the shape and area of the cross-section. be sure to include the properties of quadrilaterals and the mathematical computations necessary to support your answers

Answer 1

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

What is the explanation for the submission above?

Note that the Area of the cross-section = 16 sqrt(2) = 22.63 sq. units. The justification for this is the properties of the Cubes.

• The top face ABCD is parallel and congruent to the bottom face EFGH....(A)

• Also, sides AE and CH are perpendicular to faces ABCD and EFGH ....(B)

Mathematically, we can righty state that Diagonals AC and EH are congruent .....(C)

Given the justification by (A), congruent top and bottom faces, let us look at the cross-section ACHE.

AC is congruent and parallel to  EH   (A) & (C)

EA & HC are perpendicular to AC      (B)

Hence, the quadrilateral ACHE is a rectangle.

Step 2

Length of diagonal AC = sqrt(4^2+4^2) = 4 sqrt(2)  Pythagoras theorem.

AE = CH = DG = 4    We state this because the of the properties of cube, all sides equal;

Hence, the Area of ACHE = 4* 4sqrt(2) = 16 sqrt(2)

= 22.63 sq. units

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