Question

Find the surface area of a right pyramid, if its height is 8 cm and its base is a rectangle with sides of length 4 cm and 12 cm. Assume the apex is centered over the base. Round to the nearest tenth......

Answer 1

formula

Answer 2

Ready?

Answer 3

oh yes I was waiting for you :)

Answer 4

I was waiting to see if the other person were finished. I think I know what went wrong. Look at the new diagram.

Answer 5

ok

Answer 6

Look at Tri ACD.
Area of Tri ACD
We have to get the height of the triangle
by using the height of the solid.

(AH)^2 + (HG)^2 = (AG)^2
8^2 + (HG)^2 = (AG)^2
8^2 + 2^2 = (AG)^2
64 + 4 = (AG)^2
68 = (AG)^2
8.2 = AG

Answer 7

Agree?

Answer 8

agreed

Answer 9

Look at triangle ACD in the improved diagram.

Answer 10

Area of Tri ACD = 1/2 (12)(8.2)
A = 6(8.2)
A = 49.2
Area of Tri ABE also = 49.2

Sum of the areas of these two congruent triangles = 98.4.

Check that before we move to the other triangles. Last time, I think I messed up by having the wrong sides labeled.

Answer 11

okay

Answer 12

Having a better diagram helps me. I should have drawn it better the first time. No worries. Live and learn.

Answer 13

Look at Triangle ABC

Answer 14

Tri ABC

To get its area, we will have to use the height of the solid )which is not the same as the altitude of triangle ABC to get the height of triangle ABC.

Look inside the pyramid.

8^2 + (HF)^2 = (AF)^2
8^2 + 6^2 = (AF)^2
64 + 36 = (AF)^2
100 = (AF)^2
10 = AF

Agree?

Answer 15

agreed

Answer 16

Area Tri ABC = (1/2) bh
A = (1/2) (BC) * 10
A = (1/2) *4*10
A = 20

There are 2 of these triangles with the same area.

Tri AED also has area 20.

Total of the two is 40.

Agree?

Answer 17

Okay I see.

Answer 18

Alrighty, we are in the home stretch - we've been there before. :) But, this is the way learning goes. So, when you do your Geometry problems, always begin with detailed skeetch with all the given on it. Learn from my errors.

Answer 19

The bottom of the pyramid is a 12 by 4 = 48 square units of area rectangle.

So, the surface area of the pyramid is 48 + 98.4 + 40 = 186.4 cubic units.

See if you agree.

Answer 20

I see, got it.

Answer 21

Remember the words about always having a good diagram. And, if you ever feel you can't do math, remember that you CAN do math. There's nobody born who is good in math. It's working and sticking with it. I kinda like the adventure.

Answer 22

Thank You so much!

Answer 23

You are welcome. We'll crank out another one of these problems soon. Suggestion. Start with this same problem from scratch and see if you can work it out for yourself. If you get lost, you can always look at this solution to see where to pick up. That is the way I studied mathematics. Practice ups performance.

Answer 24

Okay, that is fine. I will take a leave for now its late.
Thank you again.