Question

Help. I need to explain if she’s right or not

Answer 1

The triangular pyramid is made of 4 congruent triangles. They all have the same shape and size, so they have the same area. The area of one triangle is

A = b*h/2
A = 5*4.3/2
A = 10.75

So four of them lead to a total surface area of 4*10.75 = 43 square meters

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The rectangular prism has the dimensions
L = 5
W = 5
H = 4.3

The surface area is found through the formula below
SA = 2*(L*W+L*H+W*H)
SA = 2*(5*5+5*4.3+5*4.3)
SA = 136

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So far we found that
surface area of pyramid = 43 square meters
surface area of prism = 136 square meters

Dividing the values, we get 136/43 = 3.16279 approximately. The result is not equal to 2, so Susan's statement is not correct. The prism has more than twice the surface area of the pyramid

Answer 2

The pyramid has 4 faces, each of which has an area that is 1/2*4.3*5 m^2.

The prism has 4 faces that have an area of 4.3*5 m^2 (double the area of the triangular faces) in addition to 2 faces that have an area of 5*5 m^2.

The prism must have an area more than double that of the pyramid, as it has additional faces beyond those that have double the area of the pyramid.