Answer:
$57
Step-by-step explanation:
We can find the cost of the custom cake by:
- splitting it into smaller rectangles
- finding the area of each one
- adding all of the rectangles' areas together
- multiplying its area by the price per square inch
1) We can split the rectangle into 3 smaller rectangles, as shown in the attached image.
2) We can find the area of each rectangle using the formula:
[tex]A = l \cdot w[/tex]
where [tex]l[/tex] = length and [tex]w[/tex] = width.
Left Rectangle
[tex]A_L = (7\text{ in}) \cdot (8\text{ in})[/tex]
[tex]A_L = 56\text{ in}^2[/tex]
Middle Rectangle
[tex]A_M = \left(\dfrac{}{}(15 - 7 - 5)\text{ in}\dfrac{}{}\right) \cdot \left(\dfrac{}{}(8 - 2)\text{ in}\\\dfrac{}{}\right)[/tex]
[tex]A_M = (3\text{ in}) \cdot (6\text{ in})[/tex]
[tex]A_m=18\text{ in}^2[/tex]
Right Rectangle
[tex]A_R = (5\text{ in})\cdot (8\text{ in})[/tex]
[tex]A_R = 40\text{ in}^2[/tex]
3) We can add together the smaller rectangles' areas:
[tex]A = A_L + A_M + A_R[/tex]
[tex]A = (56\text{ in}^2) + (18\text{ in}^2) + (40\text{ in}^2)[/tex]
[tex]A = 114\text{ in}^2[/tex]
4) We can multiply the area by the price per square inch:
[tex]P = (114\not\!\!\!\!\text{ in}^2) \cdot \dfrac{\$0.50}{1\not \!\!\!\!\text{ in}^2}[/tex]
[tex]\boxed{P = \$57}[/tex]
So, the bakery will charge $57 for the cake.
