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

Cross section is a rectangle.

Area of cross section = 16 sqrt(2) = 22.63 sq. units (to 2 decimals)

Step-by-step explanation:

Given a cube.

top face ABCD is parallel and congruent to bottom face EFGH  (1)

justified by the properties of cubes

Sides AE and CH are perpendicular to faces ABCD and EFGH (2)

justified by the properties of cubes

Diagonals AC and EH are congruent (3)

justified by (1), congruent top and bottom faces  

Consider cross-section ACHE

AC is congruent and parallel to  EH   (1) & (3)

EA & HC are perpendicular to AC      (2)

Therefore the quadrilateral ACHE is a rectangle.

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

AE = CH = DG = 4      properties of cube, all sides equal

Area of ACHE = 4* 4sqrt(2) = 16 sqrt(2) = 22.63 sq. units

rick has $1400 and sally has $1500

step-by-step explanation:

to find amount of money rick has after 10 years :

principal = $1000 , time = 10 years , rate = 4% annually

to find amount of money sally has after 10 years :

her friend gives to pay her $50 per year, therefore money she has after 10 years = 50 × 10 = $500

also, sally gets $1000 after 10 years,

therefore, total amount of money sally has after 10 years = 500 + 1000 = $1500

so, after 10 years : rick has $1400 and sally has $1500

pla·gia·rism

/ˈplājəˌrizəm/

learn to pronounce

noun

the practice of taking someone else's work or ideas and passing them off as one's own.

step-by-step explanation: