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Isosceles triangle folded question?

When an isosceles triangle is folded so that its vertex is on the midpoint of the base, a trapezoid with an area of 12 square units is formed.Find the area of the original triangle.

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Kristen B. | BS in Chemistry / Strong Math BackgroundBS in Chemistry / Strong Math Background
5.0 5.0 (59 lesson ratings) (59)
Hi Crystal.  To answer this question we need to visualize the triangle. 
Lets Label the triangle ABC, with sides AB = BC. 
When you fold the vertex down to the midpoint of the base, you create a trapezoid made of three identical triangles. 
Lets label the top of the trapezoid DE and the midpoint of the base becomes B.
Since you are folding the triangle in half, we know that AD=DB and that BE=EC.  Since each of these newly formed isosceles triangles are equal, we can use this information to find the area of one triangle from the area of the trapezoid. 
The area of the trapezoid equals 12 units2 divided by our three triangles means each triangle has an area of 4 units2.
We know that the original triangle contains four of the smaller triangles (three in the trapezoid and one overlapping from folding) we can show that the area of the original isosceles triangle is 16 units2.
Hope that helps.