Transcript Document

How do you calculate the
exact amount of wrapping
paper needed to wrap a
shoe box?
In this lesson you will learn
how to find the surface area
of a rectangular prism by
analyzing the prism’s six
faces, and computing their
areas.
Let’s Review
Surface area is the sum of the areas
of the faces on a 3D solid.
Let’s Review
We find the area of a rectangle by
multiplying its length (L) by its width (W).
rectangle area = length • width
A=L•W
Core Lesson
What is the surface area of this
rectangular prism?
6 in.
8 in.
3 in.
6 in.
8 in.
3 in.
8 in.
6
3 in.
Core Lesson
Rec. Prism SA = 2(sm. rec.) + 2 (med. rec.) + 2(lg. rec.)
= 2 (L • W) + 2 (L • W)
+
2 (L • W)
= 2 (3 • 6 )
+
2 (3 • 8)
+
2 (6 • 8)
= 2 (18)
+
2 (24)
+
2 (48)
= 36
+
48
+
96
6 in.
8 in.
3 in.
This rectangular prism has
a surface area of 180
square inches (or 180 in2).
Core Lesson
What is the surface area of this cube?
5 cm.
Core Lesson
Rec. Prism SA = 6 (square)
= 6 (s2)
= 6 (52)
= 6 (25)
5 cm.
This cube has a surface area of 150 square
centimeters (or 150 cm2).
In this lesson you have learned
how to find the surface area
of a rectangular prism by
analyzing the prism’s six faces,
and computing their areas.
Guided Practice
What is the surface area of this
rectangular prism?
2in.
10 in.
2 in.
Guided Practice
Rec. Prism SA = 2 (square) +
= 2 (L • W)
= 2 (2 • 2 )
=
2 (4)
=
8
2in.
10 in.
2 in.
+
+
+
+
4 (lg. rec.)
4 (L • W)
4 (10 • 2 )
4 (20)
80
This rectangular prism has a
surface area of 88 square
inches (or 88 in2).
Extension Activities
Find a box, and measure its side lengths. Use this
information to determine precisely how much tin
foil you will need to cover all of the box’s
surfaces.
Once you’ve found your answer, ask your teacher
for exactly the correct amount of foil needed to
cover the surfaces, with no extra paper.
Were your computations correct? Why or why not?
Extension Activities
Can you think of two different rectangular
prisms that have the same surface area?
What are their dimensions?
Be prepared to explain how you found
your answer.
Quick Quiz
What is the surface area of this prism?
7 ft
6 ft
2 ft
How many square yards of paper would be
needed to wrap this cube?
10 yd