CK-12 Geometry-Concepts

http://www.ck12.org Chapter 11. Surface Area and Volume

3. Recall that a regular hexagon is divided up into six equilateral triangles. The height of one of those triangles
   would be the apothem. If each side is 6, then half of that is 3 and half of an equilateral triangle is a 30-60-90 triangle.
   Therefore, the apothem is going to be 3

√

3. The area of the base is:

B=

1

2

(

3

√

3

)

( 6 )( 6 ) = 54

√

3 units^2

And the volume will be:

V=Bh=

(

54

√

3

)

( 15 ) = 810

√

3 units^3

4. This is an oblique right trapezoidal prism. First, find the area of the trapezoid.

B=

1

2

( 9 )( 8 + 4 ) = 9 ( 6 ) = 54 cm^2

Then, multiply this by the height.

V= 54 ( 15 ) = 810 cm^3

Explore More

Use the right triangular prism to answer questions 1-5.

1. What shape are the bases of this prism? What are their areas?


2. What are the dimensions of each of the lateral faces? What are their areas?


3. Find the lateral surface area of the prism.


4. Find the total surface area of the prism.


5. Find the total volume of the prism.
   6.WritingDescribe the difference between lateral surface area and total surface area.


6. Fuzzy dice are cubes with 4 inch sides.