Answer: 27
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Explanation:
See the attached image. I've plotted the points A, B, C, D and E as shown in the figure. Then I connected point B to point D
Rectangle ABDE attaches to triangle BDC at the shared segment BD. We don't know what BD is, so call it h for now
Notice how triangle BDC is a right triangle with the 90 degree angle at angle D. With this triangle, we know the horizontal leg is 4 units (ED+DC = EC; 7+4 = 11), the vertical leg is h, and the hypotenuse is 5.
So basically
a = 4
b = h
c = 5
Using the pythagorean theorem, we find that
a^2 + b^2 = c^2
4^2 + h^2 = 5^2
16 + h^2 = 25
h^2 = 25-16
h^2 = 9
h = sqrt(9)
h = 3
The length of BD is 3 units. So the height is 3 units
From here, you can compute the area of the rectangle to get
A = L*W = 7*3 = 21
and the area of the triangle
A = b*h/2 = 4*3/2 = 12/2 = 6
Getting the answer of 21+6 = 27
Or you can use the trapezoid area formula to get the same result
A = h*(b1+b2)/2
A = 3*(7+11)/2
A = 3*18/2
A = 54/2
A = 27
Either way, the answer is 27
