The area of a rectangle is 

. 

So for this you just multiple those two values together to get,

 .

Remeber that the units of area are squared.

The area of a triangle is 

.  

 is equal to the base multiplied by the height.  

So you still need to multiple by  or divide by .

This gives you an actual area of .

Therefore the statement is false.

The reasoning for the answer can best be seen by adding two more lines as shown in purple in the diagram below:

The target is now divided into sixteen squares of equal size, four of which are blue. This makes the probability that the dart will land in the blue region

.

Call the radius of one of the smaller quarter-circles 1 (the reasoning is independent of the actual radius). Then the area of each quarter-circle is

.

Each of the four wedges of one such quarter-circle has area 

.

The yellow region is one such wedge.

The radius of each of the larger quarter-circles is 2, so the area of each is 

The total area of the target is

Therefore, the yellow wedge is

of the target, and the odds against the dart landing in that region are 39 to 1.

One half of an inch represents  miles of real distance, so one inch represents twice this, or miles.

If we let represent the width of the county as represented on the map, then, since the county is 45 miles wide, the proportion statement for map inches and real miles is

So

  inches.

By similar reasoning, the height of the county as represented on the map is

.

The area is the product of these dimensions, which is

The answer to this question can be seen if we just rearrange the wedges of this target. If we exchange the upper right red wedge with the lower left green wedge, and the upper left green and blue wedges with the lower right red wedges, the target looks like this:

It can be seen that the probability of the dart landing in the red region of this target is , since exactly half this target is red. This is the same probability of the dart landing in the red region in the original target.

Call the radius of one of the smaller quarter-circles 1 (the reasoning is independent of the actual radius). Then the area of each quarter-circle is

.

Each of the four wedges of one such quarter-circle has area 

.

The radius of each of the larger quarter-circles is 2, so the area of each is 

Each of the three wedges of one such quarter-circle has area 

.

The blue regions comprise one larger wedge and one smaller wedge; their total area is 

The total area of the target is

The blue regions together comprise 

of the area of the circle, making this the probability the dart will land in a blue region.

To find the area of the figure above, we need to slip the figure into two rectangles. 

Using our area formula, , we can solve for the area of both of our rectangles

To find our final answer, we need to add the areas together. 

To find the area of the figure above, we need to slip the figure into two rectangles. 

Using our area formula, , we can solve for the area of both of our rectangles

To find our final answer, we need to add the areas together. 

To find the area of the figure above, we need to slip the figure into two rectangles. 

Using our area formula, , we can solve for the area of both of our rectangles

To find our final answer, we need to add the areas together.