Answer:
80 ft^2
Step-by-step explanation:
Let's start with the pentagon:
To solve for the area of a pentagon, you must calculate the area of each triangle and multiply it by 5 (the number of triangles)
The formula to calculate a triangle is 1/2 b * h, or in the format of the question, (s * h)/2.
We know the side length of one triangle is 7, and the height is 6. Since we're given this information, the rest should be simple to solve.
Process:
A = 5((s*h)/2)
s = 7
h = 6
A = 5((7*6)/2)
A = 5(42)/2)
A = 5(21)
*21 is the area of one triangle. Once you multiply 21 by 5, you'll get the area of the entire pentagon
A = 105 ft.^2
Keep in mind, this is the area of the entire pentagon. Now, the question also states that the tree takes up 25 square feet of the pentagon's area. Thank the question for making this even more simple! They've given us the area of the circle already! :)
All we need to do is subtract the area of the tree from the area of the pentagon.
Process (cont'd):
P = 105
T = 25
A = P - T
A = 105 - 25
A = 80 ft^2
So there we have it! Our final answer that tells us how many square feet of carpeting Peter needs.
Hope this helps!
