Question

What is the surface area of this right rectangular prism? Enter your answer in the box. cm² A rectangular prism with a length of 5 centimeters, a width of 4 centimeters, and a height of 7 centimeters.

Answer 1

166 cm²

Explanation:

There are two of each face on a rectangular prism. This means there will be two faces that are rectangles with dimensions of 5 by 4; this makes the area of each 5(4) = 20, giving us a total of 20(2) = 40 for these two faces.

There will be two faces that are rectangles with dimensions of 5 by 7; this makes the area of each 5(7) = 35, giving us a total of 35(2) = 70 for these two faces.

There will be two faces that are rectangles with dimensions of 4 by 7; this makes the area of each 4(7) = 28, giving us a total of 28(2) = 56 for these two faces.

This makes the total surface area

40+70+56 = 110+56 = 166 cm²

Answer 2

we know that
surface area of the prism=2*area of the base+perimeter of the base*height

step 1
find the area of the base
area of the base=length* width
length=5 cm
width=4 cm
area of the base=5*4-----> 20 cm²

step 2
find the perimeter of the base
perimeter=2*[length+width]-----> 2*[5+4]----> 18 cm

step 3
height=7 cm

step 4
find the surface area
surface area of the prism=2*area of the base+perimeter of the base*height
surface area of the prism=2*20+18*7----> 166 cm²

the answer is
166 cm²