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

(a) Rectangle

Step-by-step explanation:

Given

See attachment for cube

Solving (a): Cross-section formed when lines AC and EH meets

Lines AC and EH will meet midway of lines AE and CH

So, the shape that will be formed is quadrilateral and the sides of the quadrilateral is: AE, EH, HC and CA

Where

CA is the diagonal of the top face of cube.

So:

So, we have:

Take square roots

So, we have:

The cross-section is a rectangle

Solving (b): The area of the cross-section

Solving (c): How the cross-section is determined

Copied from (a)

Lines AC and EH will meet midway of lines AE and CH

So, the shape that will be formed is quadrilateral and the sides of the quadrilateral is: AE, EH, HC and CA

sas (side angle side)

aa (angle angle)

sss(side side side)

sas find two sides with an angle in between

aa is finding two angles and the third will add up to 180

sss find all sides

step-by-step explanation: