# Math Help - Construction I

1. ## Construction I

Given a convex quadrilateral, construct a triangle whose area is the same as the area of the quadrilateral.

2. Originally Posted by MATNTRNG
Given a convex quadrilateral, construct a triangle whose area is the same as the area of the quadrilateral.
Well, if you know the quadrilateral's area, simply construct a right triangle
where the legs are a and b, such that ab/2 = quad's area

3. Originally Posted by MATNTRNG
Given (where?) a convex quadrilateral, construct a triangle whose area is the same as the area of the quadrilateral.
1. Draw a diagonal BD. Produce the side AB.

2. A parallel to BD through C crosses the line (AB) in C'. The triangle BDC' has the same area as triangle BDC.

3. Thus triangle AC'D has the same area as the quadrilateral ABCD.