SOLUTION: find the area of a rhombus with a 45 degree angle and sides of 10 ft

Question 587618: find the area of a rhombus with a 45 degree angle and sides of 10 ft
Answer by xdragonfight(116) (Show Source): You can put this solution on YOUR website!
Well, you know the formula for the area of a parellogram:
A = bh (Area = Base times the Height)
You know the base, 10. Draw the rhombus (any size will do, make it a convenient size). One of the bottom angles is 45 degrees, and the other is 135 degrees. Find the 45 degree angle (the acute, more closed angle). The base forms one side of that angle, and another side of the rhombus forms the other side of the angle. Where that other side of the rhombus goes up and touches the top of the rhombus, at that point draw an altitude down to the base. That will form a triangle, won't it? The Base, the other side of the 45 degree angle, and the altitude.
Now, you know the altitude forms a 90-degree angle with the base, right? So your triangle has an angle of 90, one of 45, and the one that is left must be 45, so they all total 180 degrees, as the angles in every triangle do.
So your triangle has two 45 degree angles. So it must be an isosceles triangle, right? It has two equal angles, and two equal sides, and the sides opposite those equal angles must be equal, right? So the two sides opposite those equal 45-degree angles are the altitude and the base. So the altitude and the base are equal, aren't they? And you already know the base is 10 feet. So the altitude must also be10 feet.
So the base is ten feet, and the altitude is 10 feet. A=bh. Can you take it from there?
Don't be afraid to go over this a few times until you see it clearly.

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