Akira receives a prize at a science fair for having the most informative project. Her trophy is in the shape of a square pyramid and is covered in shiny gold foil.
3 in
How much gold foil did it take to cover the trophy, including the bottom?
inches
Do 4 problems Oo oo
Check

This question is Incomplete because it lacks the appropriate diagram for the square pyramid. Please kindly find attached the required diagram

45 square inches

Step-by-step explanation:

From the question, we are told that the foil covers the body of the trophy including the bottom, hence the formula we would be applying =

Total Surface Area of the Square pyramid = 2bs + b²

Where s = Height of the square pyramid

b = Edge length of the square pyramid

From the attached diagram, we can see that:

s = 6 inches

b = 3 inches

Total Surface Area of the Square pyramid = 2bs + b²

= 2 × 3 × 6 + 3²

= 36 + 9

= 45 square inches.

Therefore, the amount of gold foil it took to cover the trophy, including the bottom is 45 square inches

there are lots of ways.   pick's theorem tells us if the vertices are lattice points the area a is

a = b/2 + i - 1

where b is the number of boundary lattice points and i is the number of interior lattice points.

in the figure i count b=16, i=50 so

a = 8 + 50 - 1 = 57

let's try the shoelace formula.   the area is half the sum of the cross products of the sides.  

a(-2,6)   -2(2)-6(-5) = 26

b(-5,2)   -5(-3) - 2(-2) = 19

c(-2,-3) -2(-3) - (-3)(4) = 18

d(4,-3)   4(3) - (-3)(5) = 27

e(5,3)   5(3) - 3(1) = 12

f(1,3)     1(6) - 3(-2) = 12

a(-2,6)

each of the cross products is twice the area of the triangle with the associated side and one vertex the origin. so the area of abo=26/2=13.

area = (1/2) (26 + 19 +   18 + 27 + 12 + 12) = 57

that checks!

3

step-by-step explanation:

divide 13.5 by 9 to get the scale factor. it equals 1.5

2 * 1.5 = 3