Warm Up1.) Find the area of the hexagon.
2.) If a solid has 5 faces, 8 edges, how many vertices does it have?
3.) Sketch a pentagonal pyramid.
VocabularyLateral Face – face that is not the base
Surface Area – the sum of the area of the faces.
Net – two-dimensional representation of the faces
Formula’sSurface area of a Right Prism
S = 2B + Ph = aP + Ph
Where a is the apothem of the base, B is the area of the base, P is the perimeter of the base, and h is the height of the prism.
EXAMPLE 1 Use the net of a prism
Find the surface area of a rectangular prism with height 2 centimeters, length 5 centimeters, and width 6 centimeters.
STEP 1
SOLUTION
Sketch the prism. Imagine unfolding it to make a net.
EXAMPLE 1
STEP 2
Use the net of a prism
Find the areas of the rectangles that form the faces of the prism.
STEP 3 Add the areas of all the faces to find the surface area.
The surface area of the prism is
S = 2(12) + 2(10) + 2(30) = 104 cm2.
EXAMPLE 2 Find the surface area of a right prism
SOLUTION
STEP 1 Find the perimeter and area of a base of the prism.
Perimeter P = 5(7.05)
Apothem a = √ 62 –3.5252
EXAMPLE 2
Find the surface area of the right pentagonal prism.
Find the surface area of a right prism
Each base is a regular pentagon.
≈ 4.86
= 35.25
EXAMPLE 2
STEP 2 Use the formula for the surface area that uses the apothem.
S = aP + Ph Surface area of a right prism
≈ (4.86)(35.25) + (35.25)(9) Substitute known values.
≈ 488.57 Simplify.
Find the surface area of a right prism
The surface area of the right pentagonal prism isabout 488.57 square feet.
ANSWER
2. Find the surface area of a right rectangular prism with height 7 inches, length 3 inches, and width 4 inches using (a) a net and (b) the formula for the surface area of a right prism.
for Examples 1 and 2GUIDED PRACTICE
ANSWER
(a) NET: Left and right faces: 7 4 = 28 in.2
Top and bottom faces: 3 4 = 12 in.2
Front and back faces: 3 7 = 21 in.2
S = 2(28) + 2(12) + 2(21) = 122 in.2
2. Find the surface area of a right rectangular prism with height 7 inches, length 3 inches, and width 4 inches using (a) a net and (b) the formula for the surface area of a right prism.
for Examples 1 and 2GUIDED PRACTICE
ANSWER
(b) S = 2B + Ph
= 122 in.2
= 2(3 4) + 14 7