Dianelys wraps a gift box in the shape of a square pyramid. The figure below shows a net for the gift box. How much of the wrapping paper did she use in square meters?

Answer 1

To calculate the surface area of the gift box, we need to find the area of each of the four triangular faces and the square base.

The triangle faces are all congruent and have a base of 8 cm and height of 6 cm. The formula for the area of a triangle is (1/2) x base x height. So each triangle has an area of (1/2) x 8 cm x 6 cm = 24 cm².

There are 4 triangular faces, so the total area of the triangular faces is 4 x 24 cm² = 96 cm².

The square base has a side length of 8 cm. The formula for the area of a square is side length x side length. So the area of the square base is 8 cm x 8 cm = 64 cm².

Adding the area of the triangular faces and the area of the square base gives us the total surface area of the gift box: 96 cm² + 64 cm² = 160 cm².

Since each side of the net corresponds to one face of the gift box, we need to find the area of the net to determine how much wrapping paper was used. The net has an area of 160 cm², so Dianelys used 160 square centimeters of wrapping paper, which is equal to 0.16 square meters (since 1 square meter is equal to 10,000 square centimeters).

Therefore, Dianelys used 0.16 square meters of wrapping paper.