# Thread: slant height/total area/volume problem. did i do this one right?

1. ## slant height/total area/volume problem. did i do this one right?

IS this correct. Im not so sure, especailly about c. Thanks.

A pyramid has a square base of side 10. A lateral edge of the pyramid is 13.

a) Find the slant height.
12, because of specail right triangle 5,12,13

b)Find the total area.
LA= 1/2pl
LA= 1/2 40x12
LA=240
TA=LA+B
TA=240+100
TA= 340units^3

c) Find the volume.
V=1/3Bh
V=1/3x100xh
(height h=2leg30 (12=slant edge)
12=2leg30
6=leg30
6=apothem
6^2+hieght^2=12^2
36+ h^2=144
h^2=108
h=6squarerootof3)
V=1/3x100x6(sr3) (sr= square root)
V=100/3 x 6(sr3)

2. Someone will correct me if I'm wrong, but I think c is wrong.

It should be 400 units^3

(1/3) * (area of the base) * ( height)
(1/3) * 100 * 12 = 400 units cubed

3. that is wrong 12 is not the hieght. it is the slant height

4. Originally Posted by sarahgasoline

b)Find the total area.
LA= 1/2pl
LA= 1/2 40x12
LA=240
TA=LA+B
TA=240+100
TA= 340units^3
The area of base is (10)(10)=100
The area of each triangle is (1/2)(10)(12)=60
In total we have,
100+4(60)=100+240=340

5. thats what i have! my main question was is c correct?

6. I told you I would get corrected if I was wrong.

The height of the pyrimide is sqrt(119)

So we have (1/3) * 100 * height

7. how did you get sqrt of 119? i got sqrt of 108

8. Hope this explination makes sense, it makes sense to me

9. i did that. and got sqrt108

10. s = 12 so s^2=144
You said the side of the base is 10

so r = (1/2) of 10 so r = 5 then r^2=25

144 - 25 = 119

11. yeah but your not using the base you have to use the apothem to find the hieght

12. Isn't the apothem of a regular polygon the shortest distance between the center of the polygon and the side of the polygon.

Please correct me if I am wrong but the apothem of a square is half the length of the side.

In my previous diagram r is the apothum

I get the apothem is equal to 5 units