Answer:
a = 10/3.
Step-by-step explanation:
We write the linear function as follows:
f(x) = mx + b where m is the slope and b is the y-intercept.
f(6) = 6m + b = 8
f(2) = 2m + b = 20 Subtracting these 2 equations:
4m = -12
m = -3.
and -3 * 2 + b = 20 so:
b = 20 + 6 = 26.
So we have the linear function:
f(x) = -3 x + 26
f(a) = 16 = -3 a + 26
-3 a = 16-26
a = -10 * -3 = 10/3.
Divide the pentagon into a triangle and rectangle.
Rectangle: 12in*6in=72in^2
Triangle: (12in*5in)/2=30in^2
72in^2+30in^2=102in^2
Area = 1/2 x base x height
Base = area x 2 / height
Base = 6 1/4 x 2 = 12 1/2 / 3 1/3
Base = 3 3/4 m
