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McGraw Hill Glencoe Geometry, 2012

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McGraw Hill Glencoe Geometry, 2012 View details

Study Guide and Review

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Exercise 14 Page 904

Use the formula for the lateral area and surface area of a prism.

Lateral Area: 78 cm^2
Surface Area: 122 cm^2

Practice makes perfect

Consider the given solid.

The given solid is a rectangular prism. It has a length of 11 centimeters, a height of 3 centimeters, and a width of 2 centimeters. Let's first calculate the lateral area and then the surface area.

Lateral Area

To calculate the lateral area, we can use the known formula where h is the height of the prism and P is the perimeter of the base. L=Ph We are given the length of the sides of the base. Let's calculate the perimeter of the base. P&= 11+ 2+ 11+ 2 P&= 26 The perimeter of the base is 26 centimeters. We can substitute P= 26 and h= 3 in the formula to calculate L.

L=Ph

P= 26, h= 3

L= 26( 3)

Multiply

L=78

The lateral area is 78 square centimeters.

Surface Area

To calculate the surface area of a prism, we can use the known formula where P is the perimeter of the base, h is the height, and B is the area of the base. S=Ph+2B Note the base is a rectangle, so we can calculate its area using the formula for area of a rectangle.

B=l w

l= 11, w= 2

B= 11( 2)

Multiply

B=22

The area of the base is 22 square centimeters. Earlier, we found that Ph= 78 square centimeters. Let's substitute these values into the formula for the surface area of a prism.

S=Ph+2B

Ph= 78, B= 22

S= 78+2(22)

▼

Simplify right-hand side

Multiply

S=78+44

Add terms

S=122

The surface area of the prism is 122 square centimeters.