Surface Area of a Rectangular Prism Day 1 (of 2)

Warm Up OBJECTIVE: SWBAT find the surface area of a rectangular prism Find the area of these 2-dimensional figures: 6 cm #1 11 in 8 in #2 88 in 2 36 cm 2 Radius = 10 cm Side = 20 cm #3 Challenge Question Find the area of the red region in the square to the right. 86 cm 2 Square 20 x 20 = 400 cm 2 Circle 3.14 x 10 x 10 = 314 cm 2 Square - Circle 400 cm 2 – 314 cm 2 2

Warm Up OBJECTIVE: SWBAT find the surface area of a rectangular prism Find the area of these 2-dimensional figures: 6 cm #1 11 in 8 in #2 88 in 2 Square Area = side x side Rectangle Area = length x width 36 cm 2 Radius = 10 cm Side = 20 cm #3 Challenge Question Find the area of the red region in the square to the right. 86 cm 2 Square 20 x 20 = 400 cm 2 Circle 3.14 x 10 x 10 = 314 cm 2 Square - Circle 400 cm 2 – 314 cm 2 Area of a circle = 3.14 x radius x radius 3

Getting Ready What is the name of shape A? A What is the name of shape B? C Square Cube RectangleRectangular Prism What is the name of shape C?What is the name of shape D? B D 4

Getting Ready What similarities and differences do you see between these shapes? Write one of each in your journal. A C SquareCube Rectangle Rectangular Prism B D 5

Launch - Problem For Valentine’s Day would like to pick up this building,… wrap it,… and give it to Mrs. Godzilla., Godzilla… 6

Wrapping paper is expensive! I want to use as little as possible. How could I calculate how much wrapping paper I would need to exactly cover the building without any paper overlapping? Launch - Problem 7

Wrapping paper is expensive! I want to use as little as possible. How could I calculate how much wrapping paper I would need to exactly cover the building without any paper overlapping? How might knowing the area of each side (or face) help you to find the amount of wrapping paper needed to cover the building? Launch - Problem 8

Launch - Vocabulary The exact amount of paper needed to cover a rectangular prism (or box) is called the Surface Area. To help us discover how to calculate the surface area, we need to know how many faces a rectangular prism has. 9

Side 2 Bottom Back Top Side 1 Front Length (L) Width (W) Height (H) A rectangular prism always has ____ faces, or sides. 6 Launch - Vocabulary 10 More About Faces

Extension Vocabulary Each side of a rectangular prism is called a face. A rectangular prism has six faces. 11

4 cm 2 cm 3 cm Front Back Side 1 Side 2 Top Bottom Take a couple minutes to see how many faces you can find the area of. If you can, also try to find the total surface area. Practice – Independent Example So, how do we find the surface area of this rectangular prism? Let’s try an example… 12 Scaffolding

Surface area of the rectangular prism 4 cm 2 cm 3 cm Front Side Top Front = 4 cm x 3 cm= 12 cm 2 = 4 cm x 3 cm= 12 cm 2 = 2 cm x 3 cm= 6 cm 2 = 2 cm x 3 cm= 6 cm 2 = 4 cm x 2 cm= 8 cm 2 = 4 cm x 2 cm= 8 cm 2 52 cm Back Side 2 Bottom Practice – Guided Example Back Side 1 Side 2 Top Bottom Front Top Side Bottom Back Remember: 13

Journal #1 Find the area. Area of Front: Area of Back: Area of Top: Area of Bottom: Area of Side 1: Area of Side 2: 14

Journal #2 = (8 in x 4 in) + (8 in x 4 in) + (8 in x 2 in) + (8 in x 2 in) + (8 in x 2 in) + (4 in x 2 in) = 32 in in in in in in 2 = 120 in 2 In this solved problem, there are several mistakes. Can you find them, circle them, write in the correct work, and answer the questions on the next slide? Remember: Surface Area = Area of Front + Area of Back + Area of Side 1 + Area of Side 2 +Area of Top + Area of Bottom. 15

Questions: a. Why do you multiply 8 in x 4 in twice when finding the surface area in the problem? b.Does the order you find the area of the sides matter? (For example, do you have to find the area of the front first or can you find the area of another side first and still get the same surface area?)