SOLUTION: A square of side length S and an equilateral triangle of side length S are placed inside a rectangle of length 2S and width S as shown. What fraction of the area of the rectangle

Question 1061957: A square of side length S and an equilateral triangle of side length S are placed inside a rectangle of
length 2S and width S as shown. What fraction of the area of the rectangle remains uncovered?
Image is in the link: http://prntscr.com/dkzrut
Found 2 solutions by josgarithmetic, MathTherapy:
Answer by josgarithmetic(39620) (Show Source): You can put this solution on YOUR website!
How high is the equilateral triangle?
Base is S and the length of the other two of its sides also S each. Pythagorean Theorem formula will help; imagine cutting the triangle into two parts along the altitude.

, using "a" for the altitude length.

Area of the whole rectangle:

Fraction of the area which is uncovered:

-

Substitute for a:

The simplification algebra steps are not shown here, but final result should be .

Answer by MathTherapy(10552) (Show Source): You can put this solution on YOUR website!
A square of side length S and an equilateral triangle of side length S are placed inside a rectangle of
length 2S and width S as shown. What fraction of the area of the rectangle remains uncovered?
Image is in the link: http://prntscr.com/dkzrut

Area of rectangle:
Area of square:
Area of triangle:
Area uncovered:
Fraction of area uncovered:
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