SOLUTION: Hi I have a question that I've been doing over and over again and getting the same different answer than in my textbook and I can't figure out why. The question says to find the su

Algebra ->  Surface-area -> SOLUTION: Hi I have a question that I've been doing over and over again and getting the same different answer than in my textbook and I can't figure out why. The question says to find the su      Log On


   

Question 1062168: Hi I have a question that I've been doing over and over again and getting the same different answer than in my textbook and I can't figure out why. The question says to find the surface area of a regular right angle triangular pyramid where you know the sides of the base are 12.9 cm, the distance from the centroid to the to the centre of the base is 5.6 cm, and the slant height is 7.2 cm. When I found the area of the base I did 3(12.9x5.6/2), and got 108.36, and to get the area of the 3 other equal triangles I did 3(12.9x7.2/2), and got 139.32. Then I added these together and got 247.68 cm^2. The answer at the back of my textbook says the answer is 211.4 cm^2. Please tell me where I went wrong and how to fix it. Thank you!
Found 3 solutions by math_helper, ikleyn, rothauserc:
Answer by math_helper(2461) About Me  (Show Source):
You can put this solution on YOUR website!
For the base, I get:
+h+=+sqrt%2812.9%5E2+-+6.45%5E2%29+=+11.17173+
+A_base+=+%281%2F2%29%28h%29%28b%29+=+%281%2F2%29%2811.17173%29%2812.9%29+=+72.0576+ sq in
—
For the sides:
Each face +A_face+=+%281%2F2%29%287.2%29%2812.9%29+=+46.44+ sq in
—
Total Area = 3*A_face + A_base
3*(46.44) + 72.0576 = 139.22 + 72.0576 = 211.3776 sq in

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My answer agrees with your textbook. The problem appears to be in your calculation of the area of the base. I recommend drawing the base (equilateral triangle) and figure the height yourself. The number 5.6cm may just be a distractor thrown in, I didn't use it.

Answer by ikleyn(52781) About Me  (Show Source):
You can put this solution on YOUR website!
.
Hi I have a question that I've been doing over and over again and getting the same different answer than in my textbook and I can't figure out why.
The question says to find the surface area of a regular right angle triangular pyramid where you know the sides of the base are 12.9 cm,
the distance from the centroid to the to the centre of the base is 5.6 cm, and the slant height is 7.2 cm. When I found the area of the base
I did 3(12.9x5.6/2), and got 108.36, and to get the area of the 3 other equal triangles I did 3(12.9x7.2/2), and got 139.32.
Then I added these together and got 247.68 cm^2. The answer at the back of my textbook says the answer is 211.4 cm^2.
Please tell me where I went wrong and how to fix it. Thank you!
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". . . find the surface area of a regular right angle triangular pyramid . . . "

It is wrong terminology.

" . . . regular right angle triangular pyramid . . . " does not exist.


Answer by rothauserc(4718) About Me  (Show Source):
You can put this solution on YOUR website!
All side faces are the same in this problem
:
surface area(SA) = area of base(A) + ( (1/2) * perimeter of base * slant length )
:
The base is an equilateral triangle with sides 12.9 cm
:
height = square root ( (12.9)^2 - (6.45)^2 ) = 11.17
:
A = 2 * (1/2) * 6.45 * 11.17 = 72.05
:
SA = 72.05 + ( (1/2) * 3 * 12.9 * 7.2 ) = 211.37 cm^2
: