Answer:
Step-by-step explanation:
see the attached figure to better understand the problem
step 1
Find the measure of angle KOM
In the triangle KOM
we have
Applying the law of cosines
step 2
Find the measure of the arc KM
we know that
----> by central angle
we have
so
step 3
Find the measure of angle KLM
we know that
The inscribed angle is half that of the arc comprising
we have
substitute
P(7,6), Q(1,6), R(4,2)
We have PQ parallel to the x axis. We'll call that the base,
b = 7 - 1 = 6
The altitude is then the y difference h = 6 - 2 = 4
The area is
Answer: 12 square units
In general we can use the shoelace formula for the area of any polygon given coordinates. We write the points like this:
(7,6), (1,6), (4,2)
(1,6), (4,2), (7,6)
The area is then half the absolute value of the sum of the cross products: