# TACHS Math : Geometry

## Example Questions

### Example Question #1 : Perimeter Of Triangles, Squares, And Rectangles

Find the perimeter of a square with the following side length:

Explanation:

Perimeters can be calculated by adding together the side lengths of a polygon. A square has four sides that are all the same length, therefore, we can write the following formula to solve for the perimeter.

We can rewrite this equation as the following:

In these equations the variable, , represents side length.

Substitute the known side length and solve.

### Example Question #1 : Geometry

Find the circumference of a circle with the following radius:

Explanation:

In order to find the circumference of a circle we will use the following formula:

In this equation, the variable, , represent's the circle's radius.

Substitute in for the circle's radius.

Simplify and solve.

### Example Question #2 : Geometry

A square has perimeter 24 feet. Give its area.

144 square feet

576 square feet

36 square feet

18 square feet

36 square feet

Explanation:

The perimeter of a figure is the sum of the lengths of its sides. A square comprises four sides of equal length, so, if the perimeter of the square is 24 feet, then each side has length

feet.

The area of the square is equal to the length of a side multiplied by itself, so the area of this square is

square feet.

### Example Question #2 : Area Of Squares And Rectangles

Jennifer wants to wallpaper her room which is made up for four rectangular walls each measuring at  feet by  feet. If each roll of wallpaper covers  square feet of space, how many rolls of wallpaper will Jennifer need?

Explanation:

Start by finding out the total square footage of wallpaper needed.

Find the area of one wall. Recall that in order to find the area of a rectangle, you must multiply the length by the width.

Since we have four identical walls,

Now divide this by the amount of square feet covered by each roll of wallpaper to find how many rolls are needed.

### Example Question #1 : Area Of A Circle

Find the area of a circle with the following radius:

Explanation:

The area of a circle can be calculated using the following formula:

In this formula the radius is denoted by the variable, .

Substitute in the known variables and solve for the circle's area.

### Example Question #32 : Math

Which is equal to the radius of a circle with area

Explanation:

The formula for the area  of a circle, given its radius , is . Replace with :

To find the radius , first, divide both sides by :

Now, find the square root of both sides. Since , 20 is the square root of 400, so

.

The radius of the given circle is 20.

### Example Question #1 : Area Of A Circle

To determine whether a machine on an assembly line is filling bottles with the correct amount of soda, twenty bottles are selected. The tenth bottle and every tenth bottle after that are taken off the line and examined.

This is an example of which kind of sampling?

Convenience sampling

Systematic sampling

Cluster sampling

Stratified sampling

Systematic sampling

Explanation:

The sample in this scenario is selected from the population by choosing obects that occur at regular intervals. That makes this an example of systematic sampling.

### Example Question #1 : Area Of A Circle

What is the area of a circle that has a diameter of ?

Explanation:

Recall how to find the area of a circle:

To find the length of the radius, divide the diameter by two.

Now, plug it into the equation for the area of a circle.

### Example Question #1 : Volume Of A Sphere

Calculate the volume of a sphere with the following radius: