Area of Squares and Rectangles


Troy Morris

The area of a figure is defined to be the amount of space located on the interior of a given object. More specifically, it is the number of 1 x 1 squares, of the unit being used, that will fit into the interior of the object. In this unit, we will discuss how to find the area of a given square and a given rectangle. From this, we will discover formulas in which to find the areas for these figures rather quickly .

Square - quadrilateral with 4 congruent sides and 4 right angles.

To find the area of a square, we divide it into congruent 1 x 1 squares and add up the total number squares inside the figure. This is the basic technique in finding the area of any 2 dimensional shape.

The length of each side of the square is 4 units long. When divided up equally, the square is partitioned into 16 of the 1 x 1 squares. Therefore, the area of this square is 16 square units.

1) Construct a square with the length of each side being 3 and then 5. Check to look for any patterns that may be forming.

Formula: If we take the length of one of the sides of a square and square it, or multiply it by itself, this will give us the area of the square. Therefore, Area = s^2.

2) Find the area of a square with the given side lengths: a) 8 in. b) 10 cm c) 2 ft

3) If the area of a square is 144 square meters, find the length of each side.

Rectangle - quadrilateral with both pairs of opposite side congruent and all right angles.

Finding the area of a rectangle is similar to that of a square. We must partition it into congruent 1 x 1 squares.

When all sides are not congruent, we must alter our formula in order for it to work for the rectangle. When the length of side of a rectangle is 2 and the other is 4, the number of 1 x 1 squares inside the figure is 8. It is probably obvious that the product of 2 and 4 is 8. Try other lenths to make sure this conjecture is correct.

4) Construct a rectangle that is 4 units by 8 units and find the area by partitioning the rectangle into 1 x 1 squares.

Formula - the area of a rectangle is found by multiplying the base times the height. A = bh.

5) Find the area of a rectangle with the following lengths: a) b = 4 m, h =3 m b) b = 10 in, h = 2in

6) If the area of a rectangle is 54 square cm, and the base is 9 cm, find the height.