Question

A rectangular pyramid and a rectangular prism have bases of the same dimensions as shown below. The surface area of the rectangular pyramid is 107 square inches. The height of the rectangular prism is the same as the slant height of the pyramid. What is the surface area of the rectangular prism?

214 in2

205 in2

210 in2

220 in2

Answer 1

214in2

Answer 2

How do you figure?

Answer 3

mental math

Answer 4

still need help @hang254 ?

Answer 5

yes please

Answer 6

ok just give me a few minutes

Answer 7

sure

Answer 8

Surface Area of a Rectangular Prism = 2ab + 2bc + 2ac

Surface area of Rectangular pyramid (SA) = lb + l s1 + b s2.

where,
'l' is length, 'b' is width.

s1 is the slant length of the triangles with base 'l'.

s2 is the slant length of the triangles with base 'b'.

Answer 9

here are the two formulas for each figure

Answer 10

ok

Answer 11

so we know the surface area of the rectangular pyramid right?

Answer 12

@hang254

Answer 13

hold on, i m working on it

Answer 14

ok then i will wait

Answer 15

sorry, 107

Answer 16

wait did u finish working on it ?

Answer 17

yes

Answer 18

ok so where did u get to?

Answer 19

You asked for the surface are of the rectangular pyramid, which is 107

Answer 20

ok so we use that to find the height of the rectang pyramid

Answer 21

thats where i cant figure out the problem

Answer 22

we plug all the things that we already know such as the 5 and th 6

Answer 23

is there a formula to figure that out?

Answer 24

the one that i provided above

Answer 25

what does the " l s1+b s2 " mean in the formula??

Answer 26

sorry ok

it means L s1 + B s2

L means length

B means base

Answer 27

ok

Answer 28

s1 is the slant length of the triangles with base 'l'.

s2 is the slant length of the triangles with base 'b'.

Answer 29

i dont believe i did this right but i got 41

Answer 30

6*5=30 + 6 + 5= 41

Answer 31

ok give a few minutes to check

Answer 32

sure

Answer 33

no that is not right but it is close

Answer 34

i will show u how ot do it in a sec.

Answer 35

ok, thanks

Answer 36

now since this a regular rectangular pyramid then the slant height is the same both s1 and s2 are equal

as a result i just used s for both instead of confusing u