GIVEN: AB = 5, AF = 7, and FD = 3
Add the information to the diagram



(a) Area of ABCD
Area of rectangle = (base)(height) = (10)(5) = 50


(b) Area of triangle AEF

Area of triangle = (base)(height)/2
= (7)(5)/2 = 17.5


(c) Length of BD

Since ∆ABD is a RIGHT triangle, we can apply the Pythagorean Theorem.
We get: 5² + 10² = (side BD)²
Simplify: 25 + 100 = (side BD)²
Simplify: 125 = (side BD)²
Solve: side BD = √125 = √25 x √5 = 5√5


(d) Perimeter of ABCD
Add lengths of 4 sides
Perimeter = 5 + 10 + 5 + 10 = 30

Cheers,
Brent
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How do you assume that the length of EF is the same as AB that is 5. I think that it will only be the case when EF is perpendicular to AD.

Be careful. I'm not saying that EF has length 5; I'm saying that triangle AEF has height 5 (since AB = 5).
Here's what I mean:


For more on finding the area of a triangle, you can watch this video (starting at 5:07):

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Got it! I think I have found a hole in my understanding