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Geometry for Kids6 chapters | 45 lessons

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Lesson Transcript

Instructor:
*Kadoria Burgess*

I have a Bachelor's degree in Elementary Education and Spanish. I have taught for 5 years in bilingual classrooms of various elementary grade levels.

Will it fit? Is there enough room? These questions involve the amount of area an object needs. In this lesson, you will learn how to find the surface area of a special solid figure called a right prism.

Say you just purchased a brand new aquarium as a gift for your best friend. You take it home only to realize you only have 4 square feet of wrapping paper. Oh no! How do you know if that's enough wrapping paper? That's easy - just find the surface area!

The **surface area** is the total area of a 3D object when you add together the areas of all the sides. It will tell you the amount of space that an object or solid figure will take up all around. The key to finding the surface area is to know all of the shapes that make up the object. Then, you can measure the sides of the shapes to find your surface area.

So, what shapes make up your aquarium? You may have guessed that it's a** right prism**. A right prism is made up of two identical, parallel bases on the ends, and the faces are perpendicular to the bases. The standard aquarium is a right prism because it has two square bases on the ends, and it has four rectangular faces that are perpendicular to the two bases.

It's important to remember that right prisms have no curves. Also, there are various types of right prisms. Rectangular prisms, pentagonal prisms, hexagonal prisms, and right triangular prisms are just a few examples of right prisms. The formula for finding the surface area is the same for all right prisms and is:

Surface area = 2*B* + *hP*. In this formula, *B* is the area of one of the bases, while *h* is the prism's height, and *P* is the perimeter of the base.

Now, let's explore how to find the surface area of our right rectangular prism--our aquarium.

Let's follow these steps to find the surface area of your aquarium using the formula 2*B* + *hP*:

- First, you must measure the sides of a base to find the area of one of the bases. The bases of our aquarium are square, with each side measuring 7 inches; so, to find the base of a square (
*B*), we multiply width times height.- 7 x 7 = 49

- Now, solve for the left side of the formula by multiplying the area of one base (
*B*) times 2.- 49 x 2 = 98

- Move on to the right half of the formula. Find the perimeter of the base (
*P*) by adding all of its sides.- 7 + 7 + 7 + 7 = 28

- Next, multiply the perimeter of the base (
*P*) times the height of the prism (*h*).- 28 x 15 = 420

- Lastly, add the two multiplied parts of the formula together.
- 98 + 420 = 518

So, the surface area of the aquarium would be 518 inches squared. Your sheet of wrapping paper has a surface area of 4 square feet, which equals 576 inches squared. Phew! You have more than enough gift wrap to cover the aquarium.

To review, **surface area** is the total area of a 3D object when you add together the areas of all the sides. A **right prism** is made up of two identical, parallel bases on the ends, and the faces are perpendicular to the bases. The formula for finding surface area is 2*B* + *hP* (where *B* is the area of one of the bases, *h* is the prism's height and *P* is the perimeter of the base).

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Geometry for Kids6 chapters | 45 lessons

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