Question

1. select all of the appropriate units that could describe surface area.

a. centimeters
b. square yards
c. cubic inches
d. cubic feet

1. the rectangular prism shown is 3 units high, 2 units wide, and 5 units long. what is its surface area?
2. the rectangular prism shown is 3 units high, 4 units wide, and 3 units long. what is its surface area?
3. determine the surface area of the rectangular prism.
4. determine the surface area.

Explanation:

Step1: Identify surface - area units

Surface - area is measured in square units. Centimeters is a length unit, cubic inches and cubic feet are volume units. Square yards is a square unit. So the appropriate unit for surface area is square yards.

Step2: Recall surface - area formula for rectangular prism

The formula for the surface area of a rectangular prism is $SA = 2(lw+lh + wh)$, where $l$ is length, $w$ is width and $h$ is height.

For question 2:

$l = 5$, $w = 2$, $h = 3$
$SA=2(5\times2 + 5\times3+2\times3)$
$=2(10 + 15+6)$
$=2\times31$
$=62$ square units

For question 3:

$l = 3$, $w = 4$, $h = 3$
$SA=2(3\times4+3\times3 + 4\times3)$
$=2(12 + 9+12)$
$=2\times33$
$=66$ square units

For question 4:

Assume $l = 8$, $w = 6$, $h = 4$ (by counting the small cubes)
$SA=2(8\times6+8\times4 + 6\times4)$
$=2(48+32 + 24)$
$=2\times104$
$=208$ square units

For question 5:

Assume $l = 1$, $w = 1$, $h = 5$ (by counting the small cubes)
$SA=2(1\times1+1\times5+1\times5)$
$=2(1 + 5+5)$
$=2\times11$
$=22$ square units

Answer:

1. b. Square yards
2. 62 square units
3. 66 square units
4. 208 square units
5. 22 square units