Intermediate Geometry : Intermediate Geometry

Study concepts, example questions & explanations for Intermediate Geometry

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Example Questions

Example Question #4 : How To Find The Surface Area Of A Prism

Find the surface area of the regular hexagonal prism.

5

Possible Answers:

Correct answer:

Explanation:

13

In order to find the surface area, you will need to add up the areas of each face of the prism.

This hexagonal prism has two regular hexagons as its bases.

Recall how to find the area of a regular hexagon:

Now, since we have two hexagons, we can multiply the area by  to get the area of both bases.

Next, this prism has  rectangles that make up its sides.

Recall how to find the area of a rectangle:

In this prism, the length is also the side of the hexagon, and the width of the rectangle is the height of the prism.

Now, multiply the area of the rectangle by  to find the total area of all of the sides of the prism.

Add together the area of the sides and of the bases to find the surface area of the prism.

Plug in the given values to find the surface area of the prism.

Make sure to round to  places after the decimal.

Example Question #11 : How To Find The Surface Area Of A Prism

Find the surface area of the regular hexagonal prism.

7

Possible Answers:

Correct answer:

Explanation:

13

In order to find the surface area, you will need to add up the areas of each face of the prism.

This hexagonal prism has two regular hexagons as its bases.

Recall how to find the area of a regular hexagon:

Now, since we have two hexagons, we can multiply the area by  to get the area of both bases.

Next, this prism has  rectangles that make up its sides.

Recall how to find the area of a rectangle:

In this prism, the length is also the side of the hexagon, and the width of the rectangle is the height of the prism.

Now, multiply the area of the rectangle by  to find the total area of all of the sides of the prism.

Add together the area of the sides and of the bases to find the surface area of the prism.

Plug in the given values to find the surface area of the prism.

Make sure to round to  places after the decimal.

Example Question #12 : How To Find The Surface Area Of A Prism

Find the surface area of the regular hexagonal prism.

8

Possible Answers:

Correct answer:

Explanation:

13

In order to find the surface area, you will need to add up the areas of each face of the prism.

This hexagonal prism has two regular hexagons as its bases.

Recall how to find the area of a regular hexagon:

Now, since we have two hexagons, we can multiply the area by  to get the area of both bases.

Next, this prism has  rectangles that make up its sides.

Recall how to find the area of a rectangle:

In this prism, the length is also the side of the hexagon, and the width of the rectangle is the height of the prism.

Now, multiply the area of the rectangle by  to find the total area of all of the sides of the prism.

Add together the area of the sides and of the bases to find the surface area of the prism.

Plug in the given values to find the surface area of the prism.

Make sure to round to  places after the decimal.

Example Question #13 : How To Find The Surface Area Of A Prism

Find the surface area of the regular hexagonal prism.

9

Possible Answers:

Correct answer:

Explanation:

13

In order to find the surface area, you will need to add up the areas of each face of the prism.

This hexagonal prism has two regular hexagons as its bases.

Recall how to find the area of a regular hexagon:

Now, since we have two hexagons, we can multiply the area by  to get the area of both bases.

Next, this prism has  rectangles that make up its sides.

Recall how to find the area of a rectangle:

In this prism, the length is also the side of the hexagon, and the width of the rectangle is the height of the prism.

Now, multiply the area of the rectangle by  to find the total area of all of the sides of the prism.

Add together the area of the sides and of the bases to find the surface area of the prism.

Plug in the given values to find the surface area of the prism.

Make sure to round to  places after the decimal.

Example Question #14 : How To Find The Surface Area Of A Prism

Find the surface area of the regular hexagonal prism.

10

Possible Answers:

Correct answer:

Explanation:

13

In order to find the surface area, you will need to add up the areas of each face of the prism.

This hexagonal prism has two regular hexagons as its bases.

Recall how to find the area of a regular hexagon:

Now, since we have two hexagons, we can multiply the area by  to get the area of both bases.

Next, this prism has  rectangles that make up its sides.

Recall how to find the area of a rectangle:

In this prism, the length is also the side of the hexagon, and the width of the rectangle is the height of the prism.

Now, multiply the area of the rectangle by  to find the total area of all of the sides of the prism.

Add together the area of the sides and of the bases to find the surface area of the prism.

Plug in the given values to find the surface area of the prism.

Make sure to round to  places after the decimal.

Example Question #15 : How To Find The Surface Area Of A Prism

Find the surface area of the regular hexagonal prism.

11

Possible Answers:

Correct answer:

Explanation:

13

In order to find the surface area, you will need to add up the areas of each face of the prism.

This hexagonal prism has two regular hexagons as its bases.

Recall how to find the area of a regular hexagon:

Now, since we have two hexagons, we can multiply the area by  to get the area of both bases.

Next, this prism has  rectangles that make up its sides.

Recall how to find the area of a rectangle:

In this prism, the length is also the side of the hexagon, and the width of the rectangle is the height of the prism.

Now, multiply the area of the rectangle by  to find the total area of all of the sides of the prism.

Add together the area of the sides and of the bases to find the surface area of the prism.

Plug in the given values to find the surface area of the prism.

Make sure to round to  places after the decimal.

Example Question #16 : How To Find The Surface Area Of A Prism

Find the surface area of the regular hexagonal prism.

12

Possible Answers:

Correct answer:

Explanation:

13

In order to find the surface area, you will need to add up the areas of each face of the prism.

This hexagonal prism has two regular hexagons as its bases.

Recall how to find the area of a regular hexagon:

Now, since we have two hexagons, we can multiply the area by  to get the area of both bases.

Next, this prism has  rectangles that make up its sides.

Recall how to find the area of a rectangle:

In this prism, the length is also the side of the hexagon, and the width of the rectangle is the height of the prism.

Now, multiply the area of the rectangle by  to find the total area of all of the sides of the prism.

Add together the area of the sides and of the bases to find the surface area of the prism.

Plug in the given values to find the surface area of the prism.

Make sure to round to  places after the decimal.

Example Question #11 : How To Find The Surface Area Of A Prism

Find the surface area of the regular hexagonal prism.

6

Possible Answers:

Correct answer:

Explanation:

13

In order to find the surface area, you will need to add up the areas of each face of the prism.

This hexagonal prism has two regular hexagons as its bases.

Recall how to find the area of a regular hexagon:

Now, since we have two hexagons, we can multiply the area by  to get the area of both bases.

Next, this prism has  rectangles that make up its sides.

Recall how to find the area of a rectangle:

In this prism, the length is also the side of the hexagon, and the width of the rectangle is the height of the prism.

Now, multiply the area of the rectangle by  to find the total area of all of the sides of the prism.

Add together the area of the sides and of the bases to find the surface area of the prism.

Plug in the given values to find the surface area of the prism.

Make sure to round to  places after the decimal.

Example Question #12 : How To Find The Surface Area Of A Prism

Find the surface area of the regular hexagonal prism.

1

Possible Answers:

Correct answer:

Explanation:

13

In order to find the surface area, you will need to add up the areas of each face of the prism.

This hexagonal prism has two regular hexagons as its bases.

Recall how to find the area of a regular hexagon:

Now, since we have two hexagons, we can multiply the area by  to get the area of both bases.

Next, this prism has  rectangles that make up its sides.

Recall how to find the area of a rectangle:

In this prism, the length is also the side of the hexagon, and the width of the rectangle is the height of the prism.

Now, multiply the area of the rectangle by  to find the total area of all of the sides of the prism.

Add together the area of the sides and of the bases to find the surface area of the prism.

Plug in the given values to find the surface area of the prism.

Make sure to round to  places after the decimal.

Example Question #1 : How To Find The Volume Of A Prism

A prism with a square base has a height of  feet.

If the edge of the base is  feet, what is the volume of the prism?

Possible Answers:

Correct answer:

Explanation:

The volume of a prism is given as

where

B = Area of the base

and

h = height of the prism.

Because the base is a square, we have

So plugging in the value of B that we found and h that was given in the problem we get the volume to be the following.

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