Answer:
See Below.
Step-by-step explanation:
We are given that ΔAPB and ΔAQC are equilateral triangles.
And we want to prove that PC = BQ.
Since ΔAPB and ΔAQC are equilateral triangles, this means that:
Likewise:
Since they all measure 60°.
Note that ∠PAC is the addition of the angles ∠PAB and ∠BAC. So:
Likewise:
Since ∠QAC ≅ ∠PAB:
And by substitution:
Thus:
Then by SAS Congruence:
And by CPCTC:
We can break it into two parts.
-> First, the rectangle on the bottom is made up of 2 feet x 16 feet. The formula for area of a rectangle is length times width, so in this case it is equal to 32 feet
-> Next, the triangle has sides of 10 feet, 10 feet, and 16 feet. We can calculate that the height is 6. The formula for area of a triangle is base times height divided by two, so, 48 feet
-> Last, we can add the two totals together. 32 feet + 48 feet = 80 feet giving us our final answer of 80 feet². As this answer is not pictured I am going to assume they are not including Heron's formula or other more complex formulas, leading us to the answer of "can't be determined"
Answer:
O can't be determined
Have a nice day! - <em>Note: It depends on the level of your math class for whether the answer "cannot be determined" is correct as it can be determined, just takes more effort than simple one - two-step formulas.</em>
I hope this is what you are looking for, but if not - comment! I will edit and update my answer accordingly. (ノ^∇^)
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- Heather