Exact Answers:
- Area = 150.5*sqrt(3)
- Perimeter = 57+7*sqrt(3)
Approximate Answers:
- Area = 260.673646539
- Perimeter = 69.12435565
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Explanation:
Your diagram is 100% correct. Nice work.
To get the area of the trapezoid, we could use the area of a trapezoid formula below:
A = h*(b1+b2)/2
In this case, we have,
- h = 7*sqrt(3) = height
- b1 = 18 = base1
- b2 = 25 = base2
the bases are parallel to each other. The height is always perpendicular to the base. We won't use the "14" at all.
So,
A = h*(b1+b2)/2
A = 7*sqrt(3)*(18+25)/2
A = 7*sqrt(3)*21.5
A = (7*21.5)*sqrt(3)
A = 150.5*sqrt(3)
This is the exact area.
The approximate area is roughly
150.5*sqrt(3) = 260.673646539
The units for the area are in square km, or km^2. Though your teacher said for you not to include the units.
Another way to get the area of the trapezoid is to break the diagram into a rectangle and triangle as you have done so, and then find the area of each sub-piece. Adding the two smaller areas should lead to the result shown above.
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To get the perimeter, we add up all of the exterior sides. We do not include the right-most vertical line that is 7*sqrt(3) km long because it is inside the figure. The horizontal segment that is 7 km long is part of the "25 km" segment, so we'll ignore that 7.
Adding the four exterior sides leads to:
7*sqrt(3)+18+14+25 = 57+7*sqrt(3)
This value is exact. It approximates to
57+7*sqrt(3) = 69.12435565
The units for the perimeter are in kilometers, and you won't have any exponent over the "km". While your teacher doesn't want the units, it's still handy to know what the units would be.
