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

3 in 12 in 4 in Front = 3 in x 12 in = 36 in2 Side Front Top Side Warm Up OBJECTIVE: SWBAT describe and use the shortcut to calculate the surface area of a rectangular prism. 1. Find the area of the front, side, and top of this rectangular prism. Front = 3 in x 12 in = 36 in2 Side Front Top 12 in 4 in 3 in Side = 3 in x 4 in = 12 in2 Top = 4 in x 12 in = 48 in2 2) Find the circumference and area of a circle with radius 5 cm. Radius = 5 cm C = 2πr = 2 x 3.14 x 5 cm = 31.4 cm A = πr2 = 3.14 x 5 cm x 5 cm = 78.5 cm2

Warm Up Front = 36 in2 Side = 12 in2 12 in 4 in 3 in Top = 48 in2 + OBJECTIVE: SWBAT describe and use the shortcut to calculate the surface area of a rectangular prism. 1. Find the area of the front, side, and top of this rectangular prism. Front = 36 in2 Side = 12 in2 Side Front Top 12 in 4 in 3 in Top = 48 in2 + 96 in2 Surface Area = 96 in2 …right?

Warm Up – Whole Class Review No! No! OBJECTIVE: SWBAT describe and use the shortcut to calculate the surface area of a rectangular prism. No! No! No! No! Remember, there are six faces on a rectangular prism… Front and Back Side 1 and Side 2 Top and Bottom No! 1. Find the area of the front, side, and top of this rectangular prism. No! Front = 36 in2 No! Side = 12 in2 No! No! Side Front Top 12 in 4 in 3 in No! Top = 48 in2 + 96 in2 Surface Area = 96 in2 …right?

Surface Area is the sum of all the faces. 12 Top 4 4 You can easily see all the faces when you make a net. 4 12 4 Side Side Front 3 3 3 3 12 4 4 Side Front Top 12 in 4 in 3 in Bottom 4 4 12 Back 3 3 12

Warm Up Surface Area = 192 in2 Front = 36 in2 Back = 36 in2 Side OBJECTIVE: SWBAT describe and use the shortcut to calculate the surface area of a rectangular prism. For surface area, we need to find the sum the areas of all 6 faces. 1. Find the area of the front, side, and top of this rectangular prism. Front = 36 in2 Back = 36 in2 Side = 12 in2 Side = 12 in2 Side Front Top 12 in 4 in 3 in Top = 48 in2 Bottom = 48 in2 96 in2 + Surface Area = 192 in2

Launch A formula uses only letters, numbers, and symbols to find a mathematical value. You already know area formulas for some shapes: Are you ready for some algebra?! Length (L) Width (W) Rectangle Area = L x W = LW Area = ½ b x h = ½bh Triangle base (b) Height (h) Circle radius (r) Area = 3.14 x r x r = πr2

Explore: Equation for Surface Area Try to write a formula to find the surface area using L for length, W for width, and H for height. Top Top Side 1 Front Height (h) Front Side Side Width (w) Length (l) Bottom Don’t forget that there are six faces on a rectangular prism! Back

Explore: Equation for Surface Area SA = 2 LH + WH 2 + LW 2 Area of the Front = Length x Height Area of the Back = Length x Height Area of Side 1 = Width x Height Area of Side 2 = Width x Height Area of Top = Length x Width Area of Bottom = Length x Width . Length Width Height Top Back Side 2 Side 1 Front Height (h) Bottom Width (w) Length (l)

Explore SA = SA = 2 WH +2 LW + 2 LH 2 LH + 2 WH + 2 LW One cool thing about this equation is that it doesn’t matter in what order you find the area of the faces. SA = SA = 2 WH +2 LW + 2 LH 2 LH + 2 WH + 2 LW This is an example of the Commutative Property of Addition ( a + b = b + a )

Find the surface area of this rectangular prism: Practice Find the surface area of this rectangular prism: Let’s try an example… SA = 2LH + 2WH + 2LW 6 cm 3 cm 4 cm Top Front 2 x 6 cm x 4 cm = 48 cm2 Side + 2 x 3 cm x 4 cm = 24 cm2 + . 2 x 3 cm x 6 cm = 36 cm2 108 cm2

Journal Work Take a shot at solving some of the following problems. For problems 1 – 2 …Find the Surface Area. Show your work using the formula we generated on the previous slides: SA = 2LH + 2WH + 2LW

Journal #1

Journal #2

Journal #3 Explain in words how to find the surface area of a rectangular prism.

Journal #4 Find the mistake(s) = 120 in2 = (6 in x 5 in) + (6 in x 5 in) + (3 in x 5 in) + (3 in x 5 in) + (6 in x 3 in) + (6 in x 6 in) = 30 in2 + 30 in2 + 15 in2 + 8 in2 + 18 in2 + 36 in2 = 120 in2

Journal #5 – Find the surface area.

Journal # 6 Choose one of the following and answer on your paper: 1. Explain how to find surface area. 2. Find the surface area of this rectangular prism. 3. If you aren’t sure about #1 or #2, what is confusing to you about surface area? 5 4 2 5 cm 2 cm 4 cm