Answer:
98 ft²
Step-by-step explanation:
There are a couple of ways you can think about this one. Perhaps easiest is to treat it as a square with a triangle cut out of it. The cutout triangle has a base (across the top) of 14 ft and a height of 14 ft, so its area is ...
A = (1/2)(14 ft)(14 ft) = 98 ft²
Of course the area of the square from which it is cut is ...
A = (14 ft)² = 196 ft²
So, the net area of the two triangles shown is ...
A = (196 ft²) - (98 ft²) = 98 ft²
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Another way to work this problem is to attack it directly. Let the base of the left triangle be x. Then the base of the right triangle is 14-x, and their total area is ...
A = A1 + A2 = (1/2)(x ft)(14 ft) + (1/2)((14-x) ft)(14 ft)
We can factor out 7 ft to get ...
A = (7 ft)(x ft + (14 -x) ft)
A = (7 ft)(14 ft) = 98 ft²
X= 47.5 degrees... it has to equal 100 degrees
The circumcenter is found by finding the intersection of at least 2 perpendicular bisector segments.
Find the perpendicular bisector to segment AB. This is the line y = -3.5; the idea is that you find the equation of the horizontal line through the midpoint of AB. The midpoint has a y coordinate of -3.5. This line is shown in red horizontal line in the attached image below.
The midpoint of AC is 2.5, so the perpendicular bisector to AC is x = 2.5 which is shown as the vertical green line in the same diagram.
The red and green lines cross at the location (2.5, -3.5) which is the circumcenter's location. If you were to draw a circle through all three points A, B, & C, then this circle would be centered at (2.5, -3.5)
If point D is the circumcenter, then we know this
AD = BD = CD
basically the distance from the center to any point on the triangle is the same. This is due to the fact that all radii of the same circle are the same length.
<h3>Answer: (2.5, -3.5)</h3>
note: 2.5 in fraction form is 5/2 while -3.5 in fraction form is -7/2