Problem Solving with Areas Flashcards

All 4 cards in this deck

What are the steps to form an equation from a given area with algebraic sides?

e.g. a square of side $(x+3)$ cm has area $10$ cm²

1. Write the area as an expression: $(x+3)(x+3) = 10$
2. Expand: $x^2 + 6x + 9 = 10$
3. Rearrange ready to solve: $x^2 + 6x = 1$

True or false? On a scale drawing where 1 cm represents 5 m, an area of 1 cm² on the drawing represents 5 m² in real life.

False. It represents $5^2 = 25$ m².

If the lengths in an area problem are given in mixed units (e.g. cm and m), what must you do first?

Convert all the lengths to the same unit before calculating the area.

True or false? Two rectangles with the same perimeter must have the same area.

False. Equal perimeters can give different areas (and equal areas can give different perimeters).