Question

What is the surface area of the right prism given below?

Answer 1

Notice that it has 2 triangles,
and 3 rectangles

Answer 2

Yes o:

Answer 3

Also notice that the 2 triangles are congruent (identical)

Answer 4

so start by calculating the area of one triangle

Answer 5

I notice, there bases, correct?;o

Answer 6

okay i'll solve that hold up

Answer 7

no lol, a prism always has only 2 bases

Answer 8

the triangles are the bases..

Answer 9

okay, find the area of triangle. .

Answer 10

thats why the triangles are the bases (x

Answer 11

yes !

Answer 12

Area of 1 trianlge is 30?;O

Answer 13

Correct !

Answer 14

since we have two bases,
area of bases = 30 + 30 = 60

Answer 15

next find the lateral area (rectangles)

Answer 16

finding area of bottom rectangle should be easy :
length = 14
width = 12

Area = ?

Answer 17

14?:o

Answer 18

Area of rectangle = (length) x (width)

Answer 19

oh! ok waitt 60 x 14

Answer 20

840

Answer 21

forget about area of triangles for now, we're done wid that.

Answer 22

finding area of bottom rectangle should be easy :
length = 14
width = 12

Area = 14 * 12 = 168

Answer 23

next, find the area of left rectangle

Answer 24

5 x 14?

Answer 25

Yes !

Answer 26

70

Answer 27

yes, next.. what about the slanted rectangle ?

Answer 28

14x12?:o i'm not sure about that one

Answer 29

good try, but no

Answer 30

its length is 14, correct

Answer 31

but we dont knw its width yet

Answer 32

we need to find it first

Answer 33

look at the figure again,
notice that its width is same as the `hypotenuse` of base triangle

Answer 34

apply pythagora and find it ?

Answer 35

a^2+b^2=c^2 ?:o

Answer 36

yess

Answer 37

5^2+12^2=c^2
25+144=c^2

Answer 38

169=c^2

Answer 39

Excellent ! take `square root` and find out c all the way

Answer 40

thats a big #, did it wrong ._.

Answer 41

ohhhh okay okay

Answer 42

c^2 = 13 :D

Answer 43

so its 14x13?

Answer 44

Correct !

Answer 45

So the surface area of given prism is :

Base area + lateral area

Answer 46

just add up all the areas

Answer 47

Base Area: 60
Lateral Area is 60 * 14 = 840
Surface Area: 900
?

Answer 48

nope

Answer 49

Base Area: 60
Lateral Area is : 168 + 70 + 182
Surface Area: ??

Answer 50

480?

Answer 51

wow, idk why i made this so difficult lol i looked through and saw what i kept missing (x Thankyouxx very much!

Answer 52

total surface area = 480 is correct !

Answer 53

good job :)

Answer 54

there is a simple formula for finding lateral area :

lateral area = (perimeter of base) * (height)
= (5+12+13) * (14)
= 30 * 14
= 420

Answer 55

add to it the base areas : 420 +60
you wud get the same answer : 480