A Side from the Area

Part of the Polygons & Quadrilaterals section of Coddy's Geometry journey. Lesson 36 of 59.

The area rule works backwards. When the figure gives the area and one side, the rule becomes an equation for the other side.

$Rectangle with area 40, AB = 8 and BC = w$

Here the area is 40 and AB = 8, so $40 = 8\cdot w$ . Divide both sides by 8: $w = 5$ . On the board, tap the sides, pick Area of a rectangle, and the board writes the equation from the labels.

Challenge

ABCD is a rectangle with area 54 and AB = 9. Tap the sides, pick the rule that connects them to the area, and solve the equation the board writes for x.

Then press Check.

Try it yourself

$Use the figure to find x$