Algebra with geometry

Task goals

• State a known geometric fact (an angle rule, a perimeter/area formula, a polygon angle sum, or a similar-shape scale factor) as an equation in terms of the unknown before solving it.
• Interpret labelled diagrams of rectangles, triangles, trapeziums, squares, and L-shapes so the picture drives the algebra rather than the wording alone.
• Solve the resulting equation algebraically -- a one- or two-step linear equation for most angle and perimeter problems, and a quadratic equation for some area problems.
• When an area problem gives a quadratic equation, find both roots and reject the one that does not make sense as a length (reject negative or zero side lengths).
• Check that a final answer makes sense in context -- a length is positive, and an angle is between 0 and 360 degrees.