PLEASE HELP QUICK A prism has 2 congruent hexagonal bases like the one shown. Each hexagon is made from 2 congruent isosceles trapezoids. The volume of the prism is 234 cubic units. What is the height of the prism? 3 units 4 units 6 units 8 units

Explanation:

Let's find the area of the hexagon. It's composed of two identical (aka congruent) trapezoids.

Each trapezoid has two parallel bases of 4+4 = 8 and 5 units. The height is 3. The area of one trapezoid is

area = height(base1+base2)/2

area = 3*(8+5)/2

area = 19.5

which doubles to 2*19.5 = 39 to represent the area of the entire hexagon

The volume of any prism is found through this formula

volume = (area of base)*(height of prism)

We just found the area of the base to be 39. The height is unknown, so we'll call it h. The volume is given to be 234.

We end up with this equation

234 = 39h

which solves to h = 6 after dividing both sides by 39. This prism has a height of 6 units.

6 units

Step-by-step explanation:

Area of each trapezium is...

½(a+b)h=½(5+8)3 = 39/2 square units

Area of hexagon is..

2×39/2 = 39 square units

Area of prism= cross-sectional area ×height

Where Cross-sec. area is the hexagon

234=39h

h= 234/39

h = 6 units

(2,9)

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