Polygon ABCD has the following vertices:
2 answers:
To be able to solve clearly this problem, the best thing to do is to plot the graph (see attached pic). From the graph we can see that the points form a trapezoid.
The base is formed by the segment connecting point A and point B.
While the two heights: shorter one by the segment connecting points A and D, and the longer one by the segment connecting points B and C.
The formula for area of trapezoid is given as:
A = b (h1 + h2) / 2
Where,
<span>b = base of the trapezoid = 3 – (-4) = 7</span>
h1 = shorter height = 2 – (-2) = 4
h2 = longer height = 2 – (-5) = 7
Therefore the area is:
A = 7 (4 + 7) / 2
A = 77 / 2
<span>A = 38.5 </span>
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Answer:
B. m∠B = 118°, a = 17, c = 18
Step-by-step explanation:
The answer choices all agree on the values of ∠B and c, so we only need to compute the value of side a.
We can verify angle B is ...
∠B = 180° -30° -32° = 118°
By the law of sines, ...
a/sin(A) = b/sin(B)
Multiplying by sin(A), we get ...
a = b·sin(A)/sin(B) = 30·sin(30°)/sin(118°) ≈ 16.98855
a ≈ 17.0 . . . units . . . . . matches choice B
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If you like, you can also verify side c:
c = b·sin(C)/sin(B) = 30·sin(32°)/sin(118°) ≈ 18.00512
c ≈ 18.0 . . . units
