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Big Ideas Math: Modeling Real Life, Grade 7

BI

Big Ideas Math: Modeling Real Life, Grade 7 View details

1. Surface Areas of Prisms

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Exercise 13 Page 413

Remember the formulas for the volume of a prism and the surface area of a prism.

49.2yd^2

Practice makes perfect

We want to calculate the surface area of the given prism.

To calculate the surface area of a rectangular prism, we can use the following formula. S=2l w+2l h+2wh The terms represent the area of the three possible different sized faces. Each term is multiplied by 2 because opposite faces on a rectangular prism have equal dimensions. We are given that l= 1 15, w= 5, and h= 3, so we have enough information to calculate the value of S.

S=2l w+2l h+2wh

▼

Evaluate

SubstituteValues

Substitute values

S=2( 1 15)( 5)+2( 1 15)( 3)+2( 5)( 3)

a bc=a* c+b/c

S=2 (1* 5 +1/5 )(5)+2(1* 5 +1/5 )(3)+2(5)(3)

Multiply

S=2 (5 +1/5 )(5)+2(5 +1/5 )(3)+2(5)(3)

Add terms

S=2 (6/5 )(5)+2(6/5 )(3)+2(5)(3)

CommutativePropMult

Commutative Property of Multiplication

S=2 (5)(6/5 )+2(3)(6/5 )+2(5)(3)

Multiply

S=10(6/5 )+6(6/5 )+30

MoveLeftFacToNum

a*b/c= a* b/c

S=10* 6/5+6* 6/5+30

Multiply

S=60/5+36/5+30

Since 150÷ 5=30, we can rewrite 30 as 1505. This will help us to add all the terms.

S=60/5+36/5+30

Rewrite 30 as 150/5

S=60/5+36/5+ 150/5

Add fractions

S=246/5

Calculate quotient

S=49.2

The surface area is 49.2yd^2.

Subchapter links

Try It p.410-411

Self-Assessment for Concept & Skills p.411

Self-Assessment for Problem Solving p.412

Review & Refresh p.413

Concept, Skills, & Problem Solving p.413-414