Acereal box has a length of 8 inches, a width of 1 3/4 inches, and a height of 12 1/8. what is the surface area of the box?

270 7/16 in^2.

Step-by-step explanation:

The surface area equals the sum of the  areas of 3 pairs of congruent rectangles.

These are  2 * 8 * 1 3/4 + 2 * 8 * 12 1/2 + 2 * 1 3/4 * 12 / 1/8

= 16 * 7/4  +  16 * 25/2 + 2 * 7/4 * 97/8

=  28 + 200 + 42 7/16

= 270 7/16 in^2.

we have three similar triangles, because each has a right angle and shares an angle.   let's write the angles in order: opposite to short leg, long leg, hypotenuse.

cab similar to bad similar to cbd

or as ratios,

ca: ab: cb = ba: ad: bd = cb: bd: cd

we also know

ac = ad + cd

(ad+cd): ab: cb = ba: ad: bd = cb: bd: cd

(ad+cd)/cb=cb/cd

we have cb=6, ad=5 and seek x=cd.

we reject the negative root and conclude x=4

answer: 4

step-by-step explanation: