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Glencoe Math: Course 2, Volume 2

GM

Glencoe Math: Course 2, Volume 2 View details

6. Surface Area of Prisms

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Exercise 12 Page 670

Remember the formula for the surface area of a prism.

B

Practice makes perfect

Let's see the given measurements on the rectangular prism.

To calculate the surface area of a rectangular prism with length l, width w, and height h can be calculated using the following formula. S=2 l h+2 l w+2 h w Each term has 2 in it because opposite faces on a rectangular prism have equal dimensions. We will substitute 12 12 yards for l, 8 13 yards for w, and 10 56 yards for h into the formula for the surface area and simplify.

S=2l h+2l w+2hw

SubstituteValues

Substitute values

S=2( 12 12) ( 10 56)+2( 12 12) ( 8 13)+2( 10 56)( 8 13)

▼

Write mixed number as a fraction

a bc=a* c+b/c

S = 2(12 * 2 + 1/2 ) ( 10 * 6 + 5/6 )+ 2(12 * 2 + 1/2)( 8 * 3 + 1/3 ) + 2 ( 10 * 6 + 5/6 )( 8 * 3 + 1/3 )

Multiply

S = 2(24 + 1/2 ) ( 60 + 5/6 )+ 2(24 + 1/2)( 24 + 1/3 ) + 2 ( 60 + 5/6 )( 24 + 1/3 )

Add terms

S = 2(25/2 ) ( 65/6 )+ 2(25/2)( 25/3 ) + 2 ( 65/6 )( 25/3 )

▼

Simplify right-hand side

Multiply fractions

S = 2(1625/12 ) + 2(625/6 ) + 2 ( 1625/18 )

MoveRightFacToNum

a/c* b = a* b/c

S = 3250/12 + 1250/6 + 3250/18

Use a calculator

S = 270.833333... + 208.333333... + 180.555555...

Add terms

S = 659.722222...

Round to 1 decimal place(s)

S ≈ 659.7

The surface area is about 659.7 square yards. Therefore, answer B is correct.

Subchapter links

Guided Practice p.668

Independent Practice p.669-670

H.O.T. Problems p.670

Standardized Test Practice p.670-672

Extra Practice p.671

Common Core Review p.672