Common Core: High School - Geometry : Construct Inscribed Figures (Equilateral Triangles, Squares, Regular Hexagons)
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Example Questions
Example Question #171 : Congruence
Line 
right triangle
acute triangle
obtuse triangle
equilateral triangle
right triangle
Line 
Example Question #21 : Construct Inscribed Figures (Equilateral Triangles, Squares, Regular Hexagons)
Find the side lengths of the square inscribed in the triangle. The area of the entire triangle is 20.
Since we are finding the side lengths of a square, we really only need to find one side since all sides are congruent in a square. Recall that the formula for the area of a triangle is 
First, consider the small triangle in the upper corner. This is shown below:
The area of this triangle would be
We will consider the lower two triangles combined to be the second triangle:
The area of this triangle would be
And then we need to consider a third area which is the square
The area of the square would be
To get the total area of the triangle, we can sum all three areas.
We can sub in our areas and solve for 
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All Common Core: High School - Geometry Resources
