Lucia is hoping that Angela will buy her a geometrically interesting piece of land on which he will build a mansion. Lucia has said that she will only buy the land if it costs less than $4.00 per square foot. The plot shown below is listed for $453,175. Is Angela going to be able to get this land? Explain how you found your answer. Be sure to address all four parts of the scoring guide below. Feel free to include any castle drawings that you feel may inspire Angela's architectural vision.
The picture has, 187.5 ft on top and 397.5 ft on the bottom.
On the left side is 390 ft and on the right side is 225 ft.
The image is not a square or rectangle by the way! It also has 6 sides because they are tilted.
I am extremely confused on how to solve this!! Could someone please show the steps on how to solve this problem and is their any other way that will show you how to make sure this answer is correct (something to check your answer with) thank you!
To determine if Angela will be able to get the land, we need to calculate the cost per square foot and compare it to Lucia's condition of it being less than $4.00 per square foot.
Step 1: Calculate the total area of the plot.
To do this, we can divide the plot into two triangles and a rectangle. Calculate the area of each shape separately and then sum them up.
Area of Triangle 1:
Base = (187.5 + 397.5) / 2 = 292.5 ft
Height = 390 ft
Area = (1/2) * Base * Height
Area of Triangle 2:
Base = (187.5 + 397.5) / 2 = 292.5 ft
Height = 225 ft
Area = (1/2) * Base * Height
Area of Rectangle:
Length = 187.5 ft
Width = 397.5 - 225 = 172.5 ft
Area = Length * Width
Total Area = Area of Triangle 1 + Area of Triangle 2 + Area of Rectangle
Step 2: Calculate the cost per square foot.
Divide the listed price of $453,175 by the total area calculated in Step 1.
Cost per Square Foot = Listed Price / Total Area
Step 3: Compare the cost per square foot with Lucia's condition.
Check if the cost per square foot is less than $4.00.
Step 4: Determine if Angela can get the land.
If the cost per square foot is less than $4.00, then Angela can get the land. Otherwise, Angela cannot get the land.
By following these steps, you can determine if Angela will be able to purchase the land within Lucia's given condition.