# HSPT Math : Geometry

## Example Questions

### Example Question #21 : How To Find The Area Of A Figure

On a map, one half of an inch represents  miles of real distance.

Woodley County is a perfectly rectangular region which measures 45 miles along its northern border and 40 miles along its eastern border. In terms of , what is the area of the portion of the map that would be taken up by the county?

Explanation:

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

### Example Question #21 : How To Find The Area Of A Figure

Above is a target. The radius of the smaller quarter-circles is half that of the larger quarter-circles.

A blindfolded man throws a dart is thrown at the above target. Assuming the dart hits the target, and that no skill is involved, what is the probability that the dart will land inside one of the red regions?

Explanation:

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.

### Example Question #21 : How To Find The Area Of A Figure

Above is a target. The radius of the smaller quarter-circles is half that of the larger quarter-circles.

A blindfolded man throws a dart at the above target. Assuming the dart hits the target, and that no skill is involved, what is the probability that the dart will land in a blue region?

Explanation:

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.

### Example Question #31 : How To Find The Area Of A Rectangle

What is the area of the figure below?

Explanation:

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.

### Example Question #21 : How To Find The Area Of A Figure

What is the area of the figure below?

Explanation:

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.

### Example Question #251 : Geometric Measurement: Understanding Concepts Of Area And Relating Area To Multiplication And To Addition

What is the area of the figure below?

Explanation:

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.

### Example Question #31 : How To Find The Area Of A Rectangle

What is the area of the figure below?

Explanation:

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.

### Example Question #21 : How To Find The Area Of A Figure

What is the area of the figure below?

Explanation:

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.

### Example Question #32 : How To Find The Area Of A Rectangle

What is the area of the figure below?

Explanation:

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.

### Example Question #11 : Find Areas Of Rectilinear Figures: Ccss.Math.Content.3.Md.C.7d

What is the area of the figure below?

Explanation:

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.