Question

Ian wraps a gift box in the shape of a square pyramid. The figure below shows a netfor the gift box.

Answer 1

Since we want to know how much wrapping paper he used in square centimeters, we want to figure the total surface area of the gift box.

Since it is a square pyramid, the triangles of the sides are all congruent, and the base is a square.

So, tha area of the square base is the multiplication of its sides, which are equal:

`A_s=9.3\cdot9.3=86.49`

For the triangles, we can clauclate the area of one of them and multiply by 4 to get the area of all. The area of a triangle is its base multiplyed by its height divided by 2. The height is given and the base is the same as the square sides. So the area of 1 triangle is:

`A_t=(9.3\cdot9.6)/(2)=44.64`

So, the tota area is the area of the square plus 4 times the area of one triangle:

`A=86.49+4\cdot44.64=86.49+178.56=265.05`

This is already in the proper unit, so the area is 265.05 cm².