Area of Rectangle And Parallelogram

Definition

A rectangle is a type of quadrilateral that has its parallel sides equal to each other and all the four vertices are equal to 90 degrees. Hence, it is also called an equiangular quadrilateral. 

We will start with the formula for the area of a rectangle.  Recall that a rectangle is a quadrilateral with opposite sides parallel and right interior angles.

Area of a Rectangle

A=bh

b = the base of the rectangle

h = the height of the rectangle

Example :

Find the area of the figure below

reactangle

Solution :

This figure is not a single rectangle.  It can, however, be broken up into two rectangles.  We then will need to find the area of each of the rectangles and add them together to calculate the area of the whole figure.

There is more than one way to break this figure into rectangles.  We will only illustrate one below.

area of reactangle

We have shown above that we can break the shape up into a red rectangle (figure on left) and a green rectangle (figure on right).  We have the lengths of both sides of the red rectangle.  It does not matter which one we call the base and which we call the height. 

The area of the red rectangle is

A = bh

= 4 ×14

= 56

We have to do a little more work to find the area of the green rectangle. 

We know that the length of one of the sides is 8 units.  We had to find the length of the other side of the green rectangle when

we calculated the perimeter in Example 1 above. 

Its length was 7 units.

area of reactangle2

Thus the area of the green rectangle is

A = bh

= 8 × 7

= 56. 

Thus the area of the whole figure is

area of red rectangle + area of green rectangle

= 56 + 56

= 112.

In the process of calculating the area, we multiplied units times units. 

This will produce a final reading of square units (or units squared). 

Thus the area of the figure is 112 square units.  This fits well with the definition of area which is the number of square units that will cover a closed figure.

Our next formula will be for the area of a parallelogram.  A parallelogram is parallelogram a quadrilateral with opposite sides parallel.

Area of a Parallelogram

A = bh

b = the base of the parallelogram

h = the height of the parallelogram

You will notice that this is the same as the formula for the area of a rectangle.  A rectangle is just a special type of parallelogram.  The height of a parallelogram is a segment that connects the top of the parallelogram and the base of the parallelogram and is perpendicular to both the top and the base. 

In the case of a rectangle, this is the same as one of the sides of the rectangle that is perpendicular to the base.

Example :

Find the area of the figure below

Parallelogram

Solution :

In this figure, the base of the parallelogram is 15 units and the height is 6 units. 

This mean that we only need to multiply to find the area of

A = bh

= 15 × 6

= 90 square units.

You should notice that we cannot find the perimeter of this figure since we do not have the lengths of all of the sides, and we have no way to figure out the lengths of the other two sides that are not given.

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