PART 1: Find the surface area of each section.
The formula for finding the area of a triangle is A = 1/2(b)(h); where b = base length and h = height. And the formula for finding the area of a rectangle is A = (l)(w); where l = length and w = width.
I'll start with the gold triangles, which are both the same size so I only need to calculate once.
A = 1/2(b)(h)
A = 1/2(7)(8.6)
A = 1/2(60.2)
A = 30.1 cm²
Now, I'll find the area of the blue triangles.
A = 1/2(b)(h)
A = 1/2(12)(7)
A = 1/2(84)
A = 42 cm²
Now, I'll find the area of the rectangular base.
A = (l)(w)
A = (12)(7)
A = 84 cm²
PART 2: Find the amount of foil in each color needed to cover 1 ornament.
There are two gold triangles, so all we have to do is multiply the area of the gold triangle by 2.
(30.1)(2) = 60.2 cm²
There are two blue triangles, so all we have to do it multiply the area of the blue triangle by 2.
(42)(2) = 84 cm²
And Olga will need 84 cm² of black foil to cover the rectangular base.
PART 3: Find the total amount of foil needed to cover 1 ornament and then 100 ornaments.
To find the total amount of foil needed, just add the amounts found in the previous step.
60.2 + 84 + 84 = 228.2 cm²
Olga will need 228.2 cm² of foil to cover 1 ornament.
(228.2)(100) = 22820 cm²
Olga will need 22, 820 cm² of foil to cover 100 ornaments.
PART 4: Fill in the blanks to give your answer.
Surface area of black face(s) = 84 cm²
Surface area of blue face(s) = 84 cm²
Surface area of gold face(s) = 60.2 cm²
Total surface area of 1 ornament = 228.2 cm²
Total surface area of 100 ornaments = 22, 820 cm²
Hope this helps!
