a pizza restaurant charges $10.00 for a large one topping pizza in the shape of a circle with a diameter of 14 inches. To celebrate the World Series, the resturant decides to bake a pizza in the shape of home plate. The dimensions of the pizza are shown.

If the restaurant wants to charge the same price per square inch as a large one topping pizza how much should the restaurant charge for the home plate pizza. justify your answer.

The top two sides are 12 inches and the base is 17 and the remaining sides are 8.5 inches

well, I don't have a diagram, but if the pentagonal shape is just a rectangle with a triangle on top, its area is

8.5 * 17 + 1/2 * 17 * √(12^2-8.5^2) = 216.5 in^2

The round pizza has an area of 49π = 153.9 in^2

So, the cost of the home-plate pizza should be $10.00 * 216.5/153.9 = $14.07

To find out how much the restaurant should charge for the home plate pizza, we first need to calculate the area of the pizza. This will allow us to determine the price per square inch.

Let's start by calculating the area of the circle-shaped large one topping pizza.

Given that the diameter of the circle is 14 inches, we can find the radius by dividing the diameter by 2.
Radius (r) = 14 inches / 2 = 7 inches

The formula to calculate the area of a circle is: A = πr^2, where A represents the area and π is a mathematical constant approximately equal to 3.14.

Plugging in the values, we have:
A = 3.14 * (7 inches)^2
A ≈ 3.14 * 49 square inches
A ≈ 153.86 square inches (rounded to two decimal places)

Now we need to find the area of the home plate-shaped pizza. To do this, we can break it down into different shapes.

The top two sides of the home plate form a triangle. The formula to calculate the area of a triangle is: A = 0.5 * base * height.

Given that the base of the triangle is 17 inches and the height is 8.5 inches, we have:
A = 0.5 * 17 inches * 8.5 inches
A = 72.25 square inches

To find the area of the remaining sides, we can consider them as rectangles.

The formula to calculate the area of a rectangle is: A = length * width.

Given that the length of each remaining side is 8.5 inches and the width is 12 inches, we have:
A = 8.5 inches * 12 inches
A = 102 square inches (for each remaining side, as they are identical)

Since there are two remaining sides, the total area for both of them is:
Total area = 102 square inches + 102 square inches
Total area = 204 square inches

Now, to find the total area of the home plate-shaped pizza, we add the areas of the triangle and the remaining sides:
Total area = 72.25 square inches + 204 square inches
Total area = 276.25 square inches

To charge the same price per square inch as the large one topping pizza, the restaurant should set the price for the home plate pizza equal to the price of the large pizza divided by the area of the large pizza:
Price per square inch = $10.00 / 153.86 square inches
Price per square inch ≈ $0.065 or $0.07 (rounded to two decimal places)

Finally, to determine the price of the home plate pizza, we multiply the price per square inch by the area of the home plate pizza:
Price of the home plate pizza = $0.07 * 276.25 square inches
Price of the home plate pizza ≈ $19.33 or $19.30 (rounded to two decimal places)

Therefore, to maintain the same price per square inch, the restaurant should charge approximately $19.30 for the home plate pizza.