Question

A prism has a right triangle as its base with a hypotenuse that measures 15 meters and legs that measure 9 meters and 12 meters. What is the surface area of this prism if the height of the prism is 11 meters?

Answer 1

What is the area of the triangle?

Answer 2

not sure

Answer 3

Area of triangle = (base*height)/2

Answer 4

54

Answer 5

good

Answer 6

Now multiply that by the height of the prism (11) to get the volume of the prism

Answer 7

594

Answer 8

you got it

Answer 9

thats not an answer option

Answer 10

oh I misread and thought they wanted the volume...one sec

Answer 11

450 m2

486 m2

504 m2

612 m2

Answer 12

The prism looks like this

Answer 13

There's a front face and a back face which are both triangles with the same area

Answer 14

So far, we know that the front face is 54 sq meters, so the back face is also 54 sq meters

Answer 15

In total, the front and back face add to 54+54 = 108 sq meters

Answer 16

Now we do each lateral face

Face1 = (Hypotenuse)*(Prism Height)

Face2 = (Base)*(Prism Height)

Face3 = (height of triangle)*(Prism Height)

Answer 17

Making sense?

Answer 18

yes

Answer 19

So what's the area of face1?

Answer 20

165?

Answer 21

good, what about face2?

Answer 22

99

Answer 23

and face3?

Answer 24

132

Answer 25

now add up all the faces

Answer 26

396

Answer 27

that's the total lateral area, now add that to the area of the triangular faces

Answer 28

which is?

Answer 29

remember each triangular face is 54 square meters

Answer 30

so add on 54+54 = 108

Answer 31

504

Answer 32

you got it

Answer 33

thanks so much!

Answer 34

you're welcome

Answer 35

can you help on another question I'm about to post?

Answer 36

sure