Answer:
30 units ^2
Explanation:
To find the area of the shaded region, we find find the area of the large triangle and subtract the area of the unshaded triangle.
A of large triangle = 1/2 b*h
height = (6+3) = 9
The base is found by using the pythagorean theorem c^2 = a^2 + b^2
We need to find b^2
c^2 -a^2 = b^2
taking the square root on each side
sqrt(c^2 -a^2) = sqrt(b^2)
the base = sqrt(c^2 -a^2)
= sqrt( 15^2 - 9^2)
= sqrt(225-81)
= sqrt(144)
=12
Now that we know the base and the height, we can find the area
A of large triangle = 1/2 b*h
= 1/2 * 12 * 9
= 6*9 = 54
Using the rule of similar triangles
9 6
---- = ----------
12 base
We can use cross products to find the base of the smaller triangle
9* base = 12*6
9* base = 72
Divide by 9 on each side
base = 72/9 = 8
Now we can find the area of the smaller triangle
base = 8 and height = 6
A of smaller triangle = 1/2 b*h
= 1/2 *8 * 6
= 4*6 = 24
Area of the shaded region = Area large triangle - Area of small triangle
= 54-24
= 30