



 
Kristina, Try this shape. Stephen La Rocque. If you need more help, scroll down.
Determine the three variable relationships:
This diagram labels the lengths that we need to consider as well as the area Q of the large isosceles triangle. We have three variables, so we need three distinct equations to solve the problem. They are: (1) Side length: x + y = 6 (2) Equal areas: ½x^{2} = 3y (3) Total area: ½x^{2} + 3y + 3y + Q = 6^{2}. Scroll down if you still need more hints.
Get rid of y:
Now use the Quadratic Formula to solve for x. Since x is a length, we can ignore the negative solution and choose just the positive solution. Scroll down for more of the solution.
Quadratic formula: Next, we can combine equations (1) and (3) to solve for Q, the area we have been asked to find:
And finally, substitute the value for x that we calculated earlier into this expression.
Final calculation:
Solved. You can check by calculating y and the area of each triangle and seeing that they add to 36 square centimeters. Stephen.
 


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