19.2 cont.
4/4/17
Lateral area of a right prism with height ℎ and base perimeter 𝑃 is
𝐿 = 𝑃ℎ
Surface area of right prism with lateral area 𝐿 and base area 𝐵 is
𝑆 = 𝐿 + 2𝐵 or 𝑆 = 𝑃ℎ + 2𝐵
(or find the area of all the faces and add them together)
Ex: Find the lateral area and
surface area of the figure.
Step 1: Find the lateral area.
Use the lateral area formula
𝑃 = 2(8) + 2(6) = 28
(or 8 + 6 + 8 + 6)
Multiply
𝐿 = 𝑃ℎ
or find area of
lateral faces
= 28(12)
Back=8𝑥12 = 96
Front=8𝑥12 = 96
Right=6𝑥12 = 72
= 336 cm2 Left=6𝑥12 = 72
Total=336 cm2
Step 2: Find the surface area.
Use the surface area formula. 𝑆 = 𝐿 + 2𝐵
𝐵 = 6(8)
Simplify
or add the area of
the two bases
Top=6𝑥8 = 48
= 336 + 2(6)(8) Bottom=6𝑥8 = 48
= 432 cm2
Total=336 + 92
= 432cm2
A cylinder is a solid with congruent circular bases that lie in
parallel planes.
The lateral area of a cylinder is the area of the curved surface.
(which is actually a rectangle so the area is length x width but the
length is the circumference of the circular base) 𝐿 = 𝐶ℎ = 2𝜋𝑟ℎ
Surface area of a right cylinder
𝑆 = 2𝐵 + 𝐿 =
2𝐵 + 𝐶ℎ =
2𝜋𝑟 2 + 2𝜋𝑟ℎ
area of 2 circles + area of curved part
Ex: Find the lateral area and
the surface area of the figure.
Step 1:
Find the lateral area.
Lateral Area Formula
𝐿 = 2𝜋𝑟ℎ
Substitute
𝐿 = 2𝜋(3)(9)
Multiply
= 54𝜋 cm2
Step 2: Find the surface area
Surface area formula
𝑆 = 𝐿 + 2𝜋𝑟 2
Substitute
= 54𝜋 + 2𝜋(3)2
Simplify
= 72𝜋 cm2