Video Transcript
Calculate the area of the
shape.
From the figure, we can see that we
have a composite shape. And there are a number of different
ways that we could approach this problem. One way would be to divide the
shape horizontally into two rectangles. We know that the area of a
rectangle is found by multiplying its length by its width. So, we just need to determine the
dimensions of each rectangle, calculate their areas, and then add them together.
Rectangle one is actually the more
challenging of the two. So, we’ll come back to it. Let’s consider rectangle two for
now. We can see straightaway from the
figure that it has a length of 12 centimeters and a width of two centimeters. The area of rectangle two then is,
therefore, 12 multiplied by two, which is 24. And the units for this, which we’ll
include at the end, are square centimeters.
For rectangle one, we need to
determine the dimensions ourselves. Let’s consider the vertical
distance, the width of the rectangle, first of all. Now, this will be the difference
between the two sides of seven centimeters and two centimeters, the other two
vertical sides in this composite shape. So, the width of rectangle one is
seven minus two, which is five centimeters.
In the same way, the length or the
horizontal side in rectangle one can be found as the difference of 12 centimeters
and six centimeters, 12 minus six, which is equal to six. So, the area of rectangle one can
be found by multiplying six by five, which gives 30. The total area, then, is the sum of
these two values, 30 plus 24, which is 54. And the units for this area will be
square centimeters.
Now, I did say that there were
multiple approaches we could take for this problem. So, let’s consider another. Instead of dividing the shape
horizontally to find two rectangles, we could instead divide it vertically to give a
different two rectangles. We already determined the
dimensions of each of these rectangles in our first method. So, we have that the area of
rectangle one is six multiplied by seven, which is 42. And the area of rectangle two is
six multiplied by two, which is 12. The total area, then, is the sum of
these two values, giving 54 square centimeters once again.
Now, in fact, there is one final
approach we could take, which is to consider this composite shape as the difference
of two rectangles. The larger rectangle, outlined in
green, has a length of 12 centimeters and a width of seven centimeters, giving an
area of 84 square centimeters. The smaller rectangle, labeled
rectangle two, has a length of six centimeters and a width of five centimeters,
giving an area of 30 square centimeters. This time we find the total area of
our composite shape by subtracting 84 minus 30, which is 54.
