Answer:
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
