Holly made 12 pair of earrings for each of her girlfriends. To wrap the pairs individually, she creates a simple cardboard gift box to fold into a pyramid. The base is a square with side lengths 10c m. The sides are 4 equilateral triangles with side lengths 10 cm and height h. The height h is approximately 8 2/3 cm. In square centimeters, what is the minimum amount of cardboard Holly needs to create 12 gift boxes to wrap each pair of earrings individually?

3280cm²

Step-by-step explanation:

We are told the gift box is folded into a Pyramid with a square base.

Hence, we are to find the Surface Area of a square pyramid

From the question, we are given:

Length of the base of the square = 10cm

Triangle

Side length = 10cm

Height = 8 2/3 cm

A square Pyramid has 5 faces: 4 triangles and 1 square.

Step 1

Find the Area of the square

Formula = Side length² this is because all the side of a square is equal.

Length of the base = 10cm

Area of the square = (10cm) ²

= 100cm²

Step 2

Find the Area of the triangle. We are told the 4 triangles are equilateral, which means their side are equal.

Hence, for one triangle.

Area of a triangle = 1/2 * base * height

Base = side length = 10cm

Height = 8 2/3 = 8.6666666667cm

Area of a triangle = 1/2 * 10 * 8.6666666667

Area of a triangle = 43.333333333cm²

Since we have 4 triangles

We would have : 4 * 43.333333333cm²

= 173.33333333cm²

The Area of the 4 equilateral triangles =

173.33333333cm²

Step 3

The Surface area of the Square Pyramid

= Sum of the areas of all the faces.

= 100cm² + 173.33333333cm²

= 273.33333333cm²

Therefore, the minimum amount of cardboard needed to make one gift box = 273.33333333cm²

Step 4

The minimum amount of cardboard Holly needs to create 12 gift boxes to wrap each pair of earrings individually is calculated as: 12 * 273.33333333cm²

= 3280cm²