A church steeple that needs to be reshingled has the shape of a regular square pyramid. If base edges of the steeple measure 16 feet while lateral edges measure 17 feet, what is the lateral area (area to reshingle) of the steeple?

Question

cwrw238 · Answer

each face is an isosceles triangle :-

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cwrw238 · Answer

the area of each triangle = 1/2 * base * perpendicular height
                                        = 1/2 * 16 * perpendicular height

the height is calculated by using the pythagoras theorem

  h^2 = 17^2 - 16^2


multiplying this area by 4 will give you your answer

anonymous · Answer

would the answer be 4 to the square root of 33

solomonzelman · Answer

▲
          .  .
17    .      .    17
      .          .
    . _______ .
          16

If you split the bottom side, you will get 2 triangles that look like

       I.
       I  .
 ?     I    .   17   
       I      .
       -----
           8

but you don't know the 3rd side though.

17^2-8^2=225   and √225 = ±15 (but we are dealing with length of the side, and the length/do stance can not be negative, so just positive 15.

Now....
knowing that the height is 15, and the base (of the original triangle) is 16
 can you find the area ?

anonymous · Answer

would it be base times height to find the area 15x16

solomonzelman · Answer

yes, but by a triangle it is

base times height
--------------
          2

anonymous · Answer

duh yeah ok so its 120

solomonzelman · Answer

15 x 16 ÷ 2
15 x 8
120

I wrote it out, b/c I don't have a calculator -;(

you are correct.

anonymous · Answer

lol thank you

solomonzelman · Answer

You welcome !