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McGraw Hill Integrated II, 2012

MH

McGraw Hill Integrated II, 2012 View details

2. Surface Areas of Prisms and Cylinders

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Exercise 43 Page 820

The area of an equilateral triangle is s^2sqrt(3)4, where s is the side length of the triangle.

l^2sqrt(3)+6l h2 square units. See solution.

Practice makes perfect

Let's analyze a right prism with a height of h units and a base that is an equilateral triangle with sides of l units.

We are asked to find the surface area of the prism S. S=2 B+ Ph The variable B is the area of the base of the prism, P is the perimeter of the base, and h is the height of the prism. Therefore, P= 3l units. Since the area of an equilateral triangle with a side of s units is s^2sqrt(3)4, we get that B= l^2sqrt(3)4 square units. Now, let's substitute expressions into the formula for S.

S=2 B+ Ph

B= l^2sqrt(3)/4, P= 3l

S=2* l^2sqrt(3)/4+ 3l* h

▼

Simplify right-hand side

MoveLeftFacToNum

a*b/c= a* b/c

S=2* l^2sqrt(3)/4+3l* h

Multiply

S=2l^2sqrt(3)/4+3l h

a/b=.a /2./.b /2.

S=l^2sqrt(3)/2+3l h

a = 2* a/2

S=l^2sqrt(3)/2+2* 3l h/2

Multiply

S=l^2sqrt(3)/2+6l h/2

Add fractions

S=l^2sqrt(3)+6l h/2

Therefore, the formula for the surface area of the prism is l^2sqrt(3)+6l h2 square units.

Subchapter links

Exercises p.817-821