1. What is the area of the wall that surrounds the garage door?
Notice that the wall can be broken into two parts, a parallelogram and a triangle. The triangle's base would be 30 - 18 (as it is stated that the parallelogram's length is 18), while the height is shared with the rectangle's width, which is 12:
Area of triangle = 1/2bh
b = 12
h = 12
Area of triangle = (12 * 12)/2 = (144)/2 = 72 ft²
Area of parallelogram = bh
b = 18
h = 12
Area of parallelogram = (18 x 12) = 216 ft²
216 + 72 = 288 ft²
Next, find the amount missing because of the garage door. It is given that the door's area can be found by multiplying the length and side (both 9ft). Subtract the gotten number from the total amount:
Area of parallelogram = bh
b = 9
h = 9
9 x 9 = 81 ft²
288 - 81 = 207 ft²
A) 207 ft²
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First, note that there are two full rows in the bottom. This can be made into the rectangle. The rest would be solved using the triangle formula. Add the two results together at the end to get your total units.
Rectangle:
base = 9 units
height = 2 units
Area of Rectangle = base x height
= 9 x 2
= 18 units²
Triangle:
base = 9 units
height = 4 units
Area of Triangle = (base x height)/2
= (9 x 4)/2
= (36)/2
= 18 units²
Add the two areas together for your total units²:
18 + 18 = 36 units²
36 units²
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The "base" of the triangle is 3 ft greater than the <em>height</em> of the triangle. The given height is that it is 12 ft. This means that the base is 15 ft.
Use a² + b² = c² to solve for the sides:
c = hypotenuse = 21 ft
b = base = 15 ft
c² - b² = a²
21² - 15² = a²
(441) - (225) = a²
a² = 216
√a² = √216
a = √216 = 6√6
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I am not too sure if there is actual enough information that can be used to solve for this triangle. I understand that you will need the answers soon, so I will try to work on it and edit my answer later on. In my opinion, they would need to give at least one more measurement or information regarding which side is which to be able to obtain the answer. If i had to guess, I would guess as well the largest one, considering the 12 ft and 21 ft. Again, they will need to define "b", as well as what the "base" & "height" would be.
