Compound shapes with algebra

Task goals

• Split a compound shape (an L-shape, a rectangle with a rectangular hole, a kite, or a trapezium) into simpler shapes (rectangles, or two triangles) before writing any algebra.
• Write each simpler shape's area as a product (or half-product) of its labelled sides, using algebraic terms or expressions rather than numbers.
• Expand any brackets and collect like terms to reach one fully simplified expression for the area.
• Set a simplified expression equal to a given area and solve the resulting linear equation for the unknown.
• Use a solved value in a follow-up calculation, such as finding the perimeter or evaluating the expression at a different given value.