Surface Area and Volume: Surface Area and Volume of Prisms and Cylinders

Warm-Up Icon Section Warm-Up

In this section, you will be asked to use some geometry skills that you previously learned.  Let’s practice these skills before we start applying them to more difficult problems.

think icon Think & Click: Section Warm-Up

Complete the Think & Click activity by looking at each problem below, thinking about it, and then clicking on the question to reveal the solution.

1. Find the perimeter and area of the rectangle below.  Be sure to label your answers appropriately.

Rectangle with length 12 feet and width 5 feet
Rectangle

 

P = 2L + 2W
P = 2(12) + 2(5)
P = 34 ft

A = LW
A = (12)(5)
A = 60 ft²

2. Find the circumference and area of the circle below.  Be sure to label your answers appropriately.

Circle with radius 5 centimeters
Circle

 

C = 2πr
C = 2π(5)
C = 10π cm

A = πr²
A = π(5)²
A = 25π cm²

3. Find the perimeter and area of the right triangle below.  Be sure to label your answers appropriately.

Right triangle with base 12 inches and height 5 inches
Right Triangle

 

To find the perimeter, we need to know the length of the hypotenuse.

5² + 12² = x²
25 + 144 = x²
169 = x²
13 = x

P = 5 + 12 + 13
P = 30 in

A equals one-half b h; A equals one-half times 6 times 4; A equals 12 square inches

4. Find the perimeter and area of the isosceles triangle below.  Be sure to label your answers appropriately.

Isosceles Triangle with base 6 feet and legs 5 feet
Isosceles Triangle

 

P = 5 + 5 + 6
P = 16 ft

To find the area, we need to know the height.  When the height is drawn, a right triangle is made.

Isosceles Triangle with base 6 feet and legs 5 feet, height drawn making a right triangle in half
Isosceles Triangle

 

3² + h² = 5²
9 + h² = 25
h² = 16
h = 4

Isosceles Triangle with base 6 feet and legs 5 feet, height drawn making a right triangle in half