SOLUTION: Two congruent parallelograms and a square make up the composite figure with a side length of 5cm. What is the area of the figure? The figure is in the shape of a cube.

Question 1154697: Two congruent parallelograms and a square make up the composite figure with a side length of 5cm. What is the area of the figure? The figure is in the shape of a cube.
Answer by greenestamps(13200) (Show Source): You can put this solution on YOUR website!

Clearly the area of the square is 5^2 = 25.

Since the two congruent parallelograms together with the square make a figure that looks like a cube, the angles of each parallelogram are 45 and 135 degrees.

Then, since the side lengths of the parallelogram are 5, the height of each parallelogram is 5/sqrt(2), or (5/2)sqrt(2).

The area of each parallelogram (base times height) is then 5*((5/2)sqrt(2)).

And then the area of the whole figure -- square plus two parallelograms -- is 25+25sqrt(2).

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