Surface Area

Definition Surface Area – is the total number of unit squares used to cover a 3-D surface.

Rectangle A = bh Triangle A = ½ bh Circle A = πr² C = πd or 2πr Let’s start in the beginning… Before you can do surface area or volume, you have to know the following formulas. Rectangle A = bh Triangle A = ½ bh Circle A = πr² C = πd or 2πr

Surface Area What does it mean to you? Does it have anything to do with what is in the inside of the prism.? Surface area is found by finding the area of all the sides and then adding those answers up. How will the answer be labeled? Units2 because it is area!

Surface area of Prisms S = Ph + 2B Find the SA of any prism by using the basic formula for SA: S = Ph + 2B S = Surface Area P = perimeter of the base B = area of the base of the prism. h = height of prism

Rectangular Prism Using the formula S = Ph + 2B P = 4 + 4 + 6 + 6 = 20 m h = 5 Ph = lateral surface area = 20 • 5 = 100 m2 B = bh = 4 • 6 = 24 m2 Total Surface Area = 100 + 2 • 24 = 148 m2 A B C 4 in 5 in 6 in

Cube SA for a Cube = 6B Are all the faces the same? YES A How many faces are there? 6 4m Find the Surface area of one of the faces. 4 x 4 = 16 Area of one base/face * 6 96 m2 Times the number of faces SA for a Cube = 6B SA = 6 ● area of the base

Triangular Prism ∙ 2= 12 How many faces are there? 5 4 5 How many of each shape does it take to make this prism? 10 m 3 2 triangles and 3 rectangles = SA of a triangular prism How many triangles were there? 2 ½ (4 ∙ 3) = 6 ∙ 2= 12 5 ∙ 10 = 50 = front 4 ∙ 10 = 40 = back 3 ∙ 10 = 30 = bottom Find the area of the 3 rectangles. What is the final SA? SA = 132 m2

3. The back rectangle is different Find the AREA of each SURFACE 1. Top or bottom triangle: A = ½ bh A = ½ (6)(6) A = 18 2. The two dark sides are the same. A = bh A = 6(9) A = 54 Example: 8mm 9mm 6 mm 6mm 3. The back rectangle is different A = bh A = 8(9) A = 72 ADD THEM ALL UP! 18 + 18 + 54 + 54 + 72 SA = 216 mm²

Find the surface area of the triangular prism Find the surface area of the triangular prism. Using the formula S = Ph + 2B P = 3 + 8 + 9 = 20 m h = 7 Ph = lateral surface area = 20 • 7 = 140 m2 B = ½ bh = ½ 8 • 3 = 12m2 Total Surface Area = 140 + 2 • 12 = 164 m2 9 m

Cylinders S = 18π + 60 π Formula  S = 2πrh + 2πr2 What does it take to make this? 2 circles and 1 rectangle= a cylinder 6 m Formula  S = 2πrh + 2πr2 2πr = circumference of the Base 2πr2= area of the Base h = height of cylinder 10m 2 B  B = π x 32 = 9π 2 B= 18π C = 2π • 3 = 6π Lateral area 6π •h = 6π •10 = 60π + 2πrh S = 18π + 60 π  

SURFACE AREA of a CYLINDER. Imagine that you can open up a cylinder like so: You can see that the surface is made up of two circles and a rectangle. The length of the rectangle is the same as the circumference of the circle!

EXAMPLE: Round to the nearest hundredth. Top or bottom circle A = πr² A = π(3.1)² A = (9.61) π A ≈ 30.1754 Rectangle Length = Circumference C = π d C = (6.2) π C ≈ 19.468 Now add: S = 30. 1754 + 30. 1754 + 233.62 Now the area A = bh A ≈ 19.468(12) A ≈ 233.62 S ≈ 293.97 in²

Find the surface area of the rectangular prism. A. 22 in2 B. 36 in2 C. 76 in2 D. 80 in2

Find the lateral surface area of the rectangular prism.

SURFACE AREA Why should you learn about surface area? Is it something that you will ever use in everyday life? If so, who do you know that uses it? Have you ever had to use it outside of math?

TRIANGLES You can tell the base and height of a triangle by finding the right angle:

CIRCLES You must know the difference between RADIUS and DIAMETER. r d