A rectangular prism has a volume of 33 3/4 cubic inches and a height of 2 and 1/4 in what is the area of the base

The area of the base is 15 in²

Step-by-step explanation:

33 3/4 = 33.75

2 1/4 = 2.25

To calculate the area base of a rectangular prism we have to use the following formula:

a = area

v = volume  = 33.75 in³

h = height  = 2.25 in

v = a * h

we solve a

a = v / h

we replace the values that we know        

a = 33.75 in³  / 2.25 in

a = 15 in²

The area of the base is 15 in²

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:

no, her answer is not correct.   we square the lengths of all sides and then determine whether the pythagorean theorem holds here:

9² + 15² = 306.   this is not equal to the square of the longest side ( that square being 395.   answer c is correct.