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Lesson Example Discussion Quiz: Class Homework

Step-3

Title: Surface area for Prism & Sphere

Grade: 6-a Lesson: S3-L3

Explanation: Hello Students, time to practice and review the steps for the problem.

Lesson Steps

Step	Type	Explanation	Answer
1	Problem	Determine the base length of a pentagonal prism if its total area is 646 sq. ft and its height and apothem length are 11 ft and 16 ft, respectively.
2	Step	The given values are	Total area = 646 sq.ft h = 11 ft and a = 16 ft
3	Formula	Total surface area of pentagonal prism is	\$"Total surface area" = 5"ab" + 5"bh"\$
4	Step	Now plug the values in the formula	\$646 = 5 times 16 times b + 5 times b times 11\$
5	Step	After simplification	\$646 = 135 b\$
6	Step	Make it simpler	b = 4.78 ft
7	Step	Therefore the base length of a pentagonal prism is 4.78 ft.
8	SumUp	Can you summarize what you’ve understood in the above steps?
9	Choice.A	This is not correct because it likely arises from an incorrect calculation	7.48 ft
10	Choice.B	This is not correct because it likely an incorrect calculation	4.87 ft
11	Choice.C	This is not correct because it likely arises from an incorrect calculation	7.84 ft
12	Choice.D	This is correct because it correctly calculates the base length of the pentagonal prism	4.78 ft
13	Answer	Option	D
14	SumUp	Can you summarize what you’ve understood in the above steps?

Step

Type

Explanation

Answer

Problem

Determine the base length of a pentagonal prism if its total area is 646 sq. ft and its height and apothem length are 11 ft and 16 ft, respectively.

Step

The given values are

Total area = 646 sq.ft h = 11 ft and
a = 16 ft

Formula

Total surface area of pentagonal prism is

\$"Total surface area" = 5"ab" + 5"bh"\$

Step

Now plug the values in the formula

\$646 = 5 times 16 times b + 5 times b times 11\$

Step

After simplification

\$646 = 135 b\$

Step

Make it simpler

b = 4.78 ft

Step

Therefore the base length of a pentagonal prism is 4.78 ft.

SumUp

Can you summarize what you’ve understood in the above steps?

Choice.A

This is not correct because it likely arises from an incorrect calculation

7.48 ft

Choice.B

This is not correct because it likely an incorrect calculation

4.87 ft

Choice.C

This is not correct because it likely arises from an incorrect calculation

7.84 ft

Choice.D

This is correct because it correctly calculates the base length of the pentagonal prism

4.78 ft

Answer

Option

SumUp

Can you summarize what you’ve understood in the above steps?